bluuebunny/crossref_metadata_2025 huggingface dataset:
Curvature, geodesics and the Brownian motion on a Riemannian manifold II—Explosion properties
Authors: Ichihara Kanji
Published: July 2016

Let M be an n-dimensional, complete, connected and non compact Riemannian manifold and g be its metric. ΔM denotes the Laplacian on M.
On spinor exceptional representations
Authors: Benham J. W. , Hsia J. S.
Published: July 2016

Let f(x1 …, xm) be a quadratic form with integer coefficients and c ∈ Z. If f(x) = c has a solution over the real numbers and if f(x) ≡ c (mod N) is soluble for every modulus N, then at least some form h in the genus of f represents c. If m ≧ 4 one may further conclude that h belongs to the spinor genus of f. This does not hold when m = 3.
Addition theorem of Abel type for hyper-logarithms
Authors: Aomoto Kazuhiko
Published: July 2016

Several kinds of generalizations of classical Abel Theorem in algebraic curves are known, for example see [12] and [13]. It seems to the author these are all regarded as local relations among rational differential forms. In this article we shall try to generalize Abel Theorem for integrals of rational forms in some specific cases where these can be described in terms of hyper-logarithms (for the definition see [3] and [4], Theorem 2). Trigonometric functions have been generalized to higher dimensional cases by L. Schläfli who has obtained a very important variational formula related to the volume of a spherical simplex [16].
On augmented Schottky spaces and automorphic forms, II
Authors: Sato Hiroki
Published: July 2016

This is the second half of the paper entitled “On augmented Schottky spaces and automorphic forms”. In the first half, we introduced new coordinates to the Schottky space, and defined the augmented Schottky space by using the new coordinates. Furthermore we considered relations between the augmented Schottky space and Riemann surfaces with or without nodes.
The principle of limiting absorption and decay of local energy for the linearized equation of magnetogasdynamics
Authors: Tamura Hideo
Published: July 2016

The present paper is a continuation of [6] and [7] in which the principle of limiting absorption has been verified for symmetric systems of first order with long-range perturbations, but the operators considered there are of constant rank. On the other hand, operators with non-constant rank are also important in application as well as from a purely theoretical point of view. In this paper, we consider the linearized equation of magnetogasdynamics with long-range perturbation as an important example of such operators.
Random motion of strings and related stochastic evolution equations
Authors: Funaki Tadahisa
Published: July 2016

In this paper, we shall investigate the random motion of an elastic string by using the theory of infinite dimensional stochastic differential equations. The paper consists of three main parts and appendices. In the first part (§2), we shall derive a basic equation which describes the random motion of a string. Several properties of this equation will be investigated in § 3, 4 and 5. In the third part (§ 6), we shall deal with a stochastic differential equation on a Hilbert space as a generalization of the equation of the string.
On the class number of a unit lattice over a ring of real quadratic integers
Authors: Mimura Yoshio
Published: July 2016

Let K be a totally real algebraic number field. In a positive definite quadratic space over K a lattice En is called a unit lattice of rank n if En has an orthonormal basis {e1 …, en}. The class number one problem is to find n and K for which the class number of En is one. Dzewas ([1]), Nebelung ([3]), Pfeuffer ([6], [7]) and Peters ([5]) have settled this problem.
The invariant polynomial algebras for the groups ISL(n) and ISp(n)
Authors: Kaneta Hitoshi
Published: July 2016

This paper is a continuation to the previous one [3], We shall show that, for the inhomogeneous linear group ISL(n + 1, R) (resp. ISp(n, R)), the coadjoint invariant polynomial algebra is generated by one (resp. n) algebraically independent element. We shall state our results more precisely.
Generalized Maillet determinant
Authors: Okada S.
Published: July 2016

In this paper, we shall study a generalization of the Maillet determinant. hetp be an odd prime, and G = (Z/pZ)*. We shall identify any integer and its image in G if there is no fear of confusion. For any integer a, let R(a) denote an integer satisfying
On a generalization of the abstract Morse complex and its applications
Authors: Hong Suk Ho
Published: July 2016

Klingenberg refers in [4] the fact that the homology group of the spaceΛof closedH1curves on a manifold is isomorphic to that of the Morse complex. In this paper, we generalize the fact above and at the same time give a proof to it through cell decomposition method under a strong non degeneracy condition.

We first introduce so-called generalized Morse complex on a spaceXwith an action of Lie groupGand an invariant energy functionEonX. The case of the spaceΛof closed curves is obviously obtained throughG=S1.
A generalization of Hubert’s Theorem 94
Authors: Miyake Katsuya
Published: July 2016

Let k be an algebraic number field of finite degree. We denote the absolute class field of k by and the absolute ideal class group of k by Cl(k).
Une caractérisation des noyaux de convolution rèels de type logarithmique
Authors: Itô Masayuki
Published: July 2016

Soit X un groupe abélien localement compact séparé et dénombrable á l’infini. On désignera par ξ la mesure de Haar sur X. Un noyau de convolution réel N (c’est-à-dire, une mesure de Radon réelle) sur X sera dit de type logarithmique s’il existe un semi-groupe (αt)t≥0 vaguement continu, markovien et récurrent des noyaux de convolution (non-négatifs) tel que limt → ∞ (vaguement) et, pour toute (pour la notation, voir § 2),
Remark on Smith’s result on a divisor problem in arithmetic progressions
Authors: Matsumoto Kohji
Published: July 2016

Let dk(n) be the number of the factorizations of n into k positive numbers. It is known that the following asymptotic formula holds:

where r and q are co-prime integers with 0 < r < q, Pk is a polynomial of degree k − 1, φ(q) is the Euler function, and Δk(q; r) is the error term. (See Lavrik [3]).
On a generalization of Hamburger’s theorem
Authors: Yoshimoto Akinori
Published: July 2016

The relationship between Poisson’s summation formula and Hamburger’s theorem [2] which is a characterization of Riemann’s zetafunction by the functional equation was already mentioned in Ehrenpreis-Kawai [1]. There Poisson’s summation formula was obtained by the functional equation of Riemann’s zetafunction. This procedure is another proof of Hamburger’s theorem. Being interpreted in this way, Hamburger’s theorem admits various interesting generalizations, one of which is to derive, from the functional equations of the zetafunctions with Grössencharacters of the Gaussian field, Poisson’s summation formula corresponding to its ring of integers [1], The main purpose of the present paper is to give a generalization of Hamburger’s theorem to some zetafunctions with Grössencharacters in algebraic number fields. More precisely, we first define the zetafunctions with Grössencharacters corresponding to a lattice in a vector space, and show that Poisson’s summation formula yields the functional equations of them. Next, we derive Poisson’s summation formula corresponding to the lattice from the functional equations.
Remarks to the uniqueness problem of meromorphic maps into PN(C), I
Authors: Fujimoto Hirotaka
Published: July 2016

As generalizations of the results in [5] and [4], the author gave some uniqueness theorems of meromorphic maps into PN(C) in previous papers [2] and [3].
Remarks to the uniqueness problem of meromorphic maps into PN(C), II
Authors: Fujimoto Hirotaka
Published: July 2016

In [7], R. Nevanlinna gave the following uniqueness theorem of meromorphic functions as an improvement of a result of G. Pólya ([8]).

Theorem A. Let f, g be non-constant meromorphic functions on C. If there are five mutually distinct values a1, …, a5 such that f−1(ai = g−1(ai) (1 ≦ i ≦ 5), then f ≡ g.
A remark concerning the 2-adic number field
Authors: Shirai Susumu
Published: July 2016

Let Q2 be the 2-adic number field, T/Q2 be a finite unramified extension, ζv be a primitive 2v-th root of unity, and let Kv = T(ζv). In a previous paper [1, Theorem 11], we stated the following theorem without its proof.
Local energy decays for wave equations with time-dependent coefficients
Authors: Tamura Hideo
Published: July 2016

We consider the decay of the local energy for the following equation in three dimension:

(0.1) utt + but − Δu = 0

u(0, x) = f(x) and ut(0, x) = g(x).
Periodic solutions of certain nonlinear parabolic differential equations in domains with periodically moving boundaries
Authors: Yamada Yoshio
Published: July 2016

In this paper we consider the periodic problems for certain nonlinear parabolic differential equations in domains with periodically moving boundaries. The typical problem, which is going to be discussed in the present paper, is to solve the following:
Galois Group of the Maximal Abelian Extension over an Algebraic Number Field
Authors: Kubota Tomio
Published: July 2016

The aim of the present work is to determine the Galois group of the maximal abelian extensionΩAover an algebraic number fieldΩof finite degree, which we fix once for all.

Let Z be a continuous character of the Galois group ofΩA/Ω. Then, by class field theory, the character Z is also regarded as a character of the idele group of Ω. We call such Zcharacter of Ω. For our purpose, it suffices to determine the groupXlof the characters ofΩwhose orders are powers of a prime numberl.
Capacities of Borelian Sets and the Continuity of Potentials
Authors: Kishi Masanori
Published: July 2016

One of the most important problems in the potential theory is the one of capacitability, that is, whether the inner capacity of an arbitrary borelian subset B is equal to the outer capacity of B. As for the capacities induced by the Newtonian potentials and other classical potentials, Choquet [5] has shown that every borelian and, more generally, every analytic set are capacitable. He goes on as follows : first he shows that, for the Newtonian capacity f, the inequality of strong subadditivity holds, that is,

and then, using this inequality, he shows that the outer capacity f* has the analogous property to one of the outer measure, more precisely, if an increasing sequence {An} of arbitrary subsets converges to A, then f*(A) = limf*(An)- This property plays an important role in his proof.
Bergman norm estimates of Poisson integrals
Authors: Choe Boo Rim , Koo Hyungwoon , Yi Heungsu
Published: July 2016

On the half space Rn × R+, it has been known that harmonic Bergman space bp can contain a positive function only if . Thus, for , Poisson integrals can be bp-functions only by means of their boundary cancellation properties. In this paper, we describe what those cancellation properties explicitly are. Also, given such cancellation properties, we obtain weighted norm inequalities for Poisson integrals. As a consequence, under weighted integrability condition given by our weighted norm inequalities, we show that our cancellation properties are equivalent to the bp-containment of Poisson integrals for p under consideration. Our results are sharp in the sense that orders of our weights cannot be improved.
Computation ofL(0,χ) and of relative class numbers of CM-fields
Authors: Louboutin Stéphane
Published: July 2016

Let χ be a nontrivial Hecke character on a (strict) ray class group of a totally real number fieldLof discriminantdL. Then,L(0,χ) is an algebraic number of some cyclotomic number field. We develop an efficient technique for computing the exact values ats= 0 of such abelian HeckeL-functions over totally real number fieldsL. Letfχdenote the norm of the finite part of the conductor ofχ. Then, roughly speaking, we can computeL(0,χ) inO((dLfx)0.5+∊) elementary operations. We then explain how the computation of relative class numbers of CM-fields boils down to the computation of exact values ats= 0 of such abelian HeckeL-functions over totally real number fieldsL. Finally, we give examples of relative class number computations for CM-fields of large degrees based on computations ofL(0,χ) over totally real number fields of degree 2 and 6.
On the second Gaussian map for curves on a K3 surface
Authors: Colombo Elisabetta , Frediani Paola
Published: July 2016

By a theorem of Wahl, for canonically embedded curves which are hyperplane sections of K3 surfaces, the first Gaussian map is not surjective. In this paper we prove that ifCis a general hyperplane section of high genus (> 280) of a general polarized K3 surface, then the second Gaussian map ofCis surjective. The resulting bound for the genusgof a general curve with surjective second Gaussian map is decreased tog> 152.
The structure of sally modules and Buchsbaumness of associated graded rings
Authors: Ozeki Kazuho
Published: July 2016

LetAbe a Noetherian local ring with the maximal ideal m, and letIbe an m-primary ideal inA. This paper examines the equality on Hilbert coefficients ofIfirst presented by Elias and Valla, but without assuming thatAis a Cohen–Macaulay local ring. That equality is related to the Buchsbaumness of the associated graded ring ofI.
Minimal Models and Abundance for Positive Characteristic Log Surfaces
Authors: Tanaka Hiromu
Published: July 2016

We discuss the birational geometry of singular surfaces in positive characteristic. More precisely, we establish the minimal model program and the abundance theorem for ℚ-factorial surfaces and for log canonical surfaces. Moreover, in the case where the base field is the algebraic closure of a finite field, we obtain the same results under much weaker assumptions.
Some applications of Synge’s formula to the theory of several complex variables
Authors: Sasaki Takeshi , Suzuki Osamu
Published: July 2016

In [10] and [11], the second author proved the following theorem by using Synge’s formula:

THEOREM I. Let M be a kähler manifold with positive holomorphic bi-sectional curvature. Then every pseudoconvex domain in M is a Stein manifold.
On projective invariance of multi-parameter Brownian motion
Authors: Takenaka Shigeo
Published: July 2016

The multi-parameter Brownian motion introduced by P. Lévy is not only a basic random field but also gives us interesting fine probabilistic structures as well as important properties from the view point of analysis. We shall be interested in investigation of such structures and properties by expressing the Brownian motion in terms of the multiparameter white noise. The expression naturally requires basic tools from analysis, in particular the Radon transform. While there arises the special linear group SL(n + 1, R), to which the Radon transform is adapted, and the group plays an important role in observing probabilistic structures of the Brownian motion. To be more interested, we can give some deep insight to unitary representations of SL(n + 1, R) through our discussion.
Faithful Representations of Lie Groups II
Authors: Gotô Morikuni
Published: July 2016

The present paper is a continuation of Part I. In the introduction of Part I we have explained our main problems and sketched their results. In the present part we shall proceed to give complete proofs of them.
Note on an Ordering Theorem for Subfields
Authors: Nakayama Tadasi
Published: July 2016

In a recent paper [3] Tannaka gave an interesting ordering theorem for subfields of a p-adic number field, The purpose of the present note is firstly to observe, on modifying Tannaka’s argument a little, that his restriction to those subfields over which the original field is abelian may be removed and in fact the theorem holds for arbitrary fields which are not p-adic number fields, indeed in a much refined form, and secondly to formulate a similar ordering theorem for algebraic number fields in terms of idèle-class groups in place of element groups.
Sur la Théorie des Variétés Algébriques
Authors: Chevalley C.
Published: July 2016

A. Weil a généralisé la notion de variété algébrique d’un espace affine (ou projectif ) en introduisant la notion de variété abstraite (nous dirons simplement “variété” au lieu de “variété abstraite,” appelant variétés affines les variétés algébriques d’un espace affine). La définition donnée par A. Weil des variétés algébriques s’inspire manifestement de la notion de variété differentiate, conçue comme réunion d’un nombre fini de morceaux dont chacun peut être considéré comme une partie ouverte d’un espace numérique, les variétés des espaces affines se substituant aux ensembles ouverts des espaces euclidiens.
Remarks on the Elliptic Case of the Mapping Theorem for Simply-Connected Riemann Surfaces
Authors: Heins Maurice
Published: July 2016

It is well-known that the conformal equivalence of a compact simply-connected Riemann surface to the extended plane is readily established once it is shown that given a local uniformizer t(p) which carries a given point p0 of the surface into 0, there exists a function u harmonic on the surface save at p0 which admits near p0 a representation of the form

(α complex 0; h harmonic at p0). For the monodromy theorem then implies the existence of a meromorphic function on the surface whose real part is u. Such a meromorphic function has a simple pole at p0 and elsewhere is analytic. It defines a univalent conformal map of the surface onto the extended plane.
Some Remarks on Boundary Behavior of Analytic and Meromorphic Functions
Authors: Bagemihl F. , Seidel W.
Published: July 2016

This paper is concerned with regular and meromorphic functions in |z| < 1 and their behavior near |z| = 1. Among the results obtained are the following. In section 2 we prove the existence of a non-constant meromorphic function that tends to zero at every point of |z| = 1 along almost all chords of |z| < 1 terminating in that point. Section 3 deals with the impossibility of ex tending this result to regular functions. In section 4 it is shown that a regular function can tend to infinity along every member of a set of spirals approach ing |z| = 1 and exhausting |z| < 1 in a simple manner. Finally, in section 5 we prove that this set of spirals cannot be replaced by an exhaustive set of Jordan arcs terminating in points of |z| = 1; Theorem 3 of this section can be interpreted as a uniqueness theorem for meromorphic functions.
Note on Complete Cohomology of a Quasi-Frobenius Algebra
Authors: Nakayama Tadasi
Published: July 2016

Let A be a quasi-Frobenius algebra over a field K. A has a complete (co)homology theory which may be established upon an augmented acyclic projective complex, i.e. a commutative diagram

of A-double-modules with exact horizontal row, projective Xp, and with epimorphic resp. monomorphic ε and t. Negative-dimensional cohomology groups, over an A-double-module, are expected to be in close relationship with (ordinary positive-dimensional) homology groups.
A Note on Conformal Mappings of Certain Riemannian Manifolds
Authors: Kurita Minoru
Published: July 2016

The contents of this note were reported at a meeting of the Japan Mathematical Society five years ago, but it was not printed. Prof. K. Yano advised me to do so and it was as follows.
On Transitive Simple Groups of Degree 3p
Authors: Ito Noboru
Published: July 2016

Let Q be the set of symbols 1, 2,…, 3 p, where p is an prime number greater than 3. Let be a transitive permutation group on Ω, which is simple and in which the normalizer of a Sylow p-subgroup has order 2 p.
Mutual Contradiction of Two Self-Consistent Abstractions
Authors: Ono Katuzi
Published: July 2016

A vast class of abstractions are proved self-contradictory by Russell-type paradoxes in the sense that the negation of any one of them can be proved tautologically. On the other hand, there are a vast class of abstractions, each being self-consistent. A simple criterion for abstractions to be self-consistent (a sufficient condition) can be given. However, even a fairly restricted class of abstractions, each satisfying the criterion to be self-consistent, may contradict to each other.
Taboo Versus Axiom
Authors: Ono Katuzi
Published: July 2016

Some important formal systems are really developable from a finite number of axioms in the lower classical predicate logic LK or in the intuitionistic predicate logic LJ. Any system of this kind can be developed in LK (or in LJ) from the single conjunction of all the axioms of the system.
On Analytic Families of Compact Riemann Surfaces with Non-Trivial Automorphisms
Authors: Kuribayashi Akikazu
Published: July 2016

The purpose of this paper is to investigate the moduli of compact Riemann surfaces with non-trivial automorphisms.
On Systems of Self-Consistent Abstractions
Authors: Inoue Yoshinobu
Published: July 2016

In this paper, I would like to show that there are many systems of abstractions, each abstraction being self-consistent, but each system as a whole leading to contradiction or to some pathological situation.
A Lemma which Distinguishes Minimal Logics from Other Logics
Authors: Ono Katuzi
Published: July 2016

In my joint work with J. Ito [7], we have pointed out that the following property (called ASSUMPTION REMOVABILITY) is characteristic of positive logics LO, LP, and LQ:

ASSUMPTION REMOVABILITY. If → is provable for any pair of propositions andhaving no primitive notions (proposition-, predicate-, and relation-symbols) in common, thenis also provable.
On the Class Number of a Relatively Cyclic Number Field
Authors: Yokoi Hideo
Published: July 2016

Letlbe a rational prime. For eachn≧0, denote byζlna primitiveln-th root of unity and byQ(ζl,n) the cyclotomic field obtained by adjoiningζl,nto the rational field Q. Then atheoremwhich was proved by H. Weber is well known:
Sario’s Potentials and Analytic Mappings
Authors: Nakai Mitsuru
Published: July 2016

In order to extend Nevanlinna’s first and second fundamental theorems to arbitrary analytic mappings between Riemann surfaces, Sario [8, 9] introduced a kernel function on an arbitrary Riemann surface generalizing the elliptic kernel on the Riemann sphere. Because of the importance of the potential theoretic method in the value distribution theory, we discussed potentials of Sario’s kernel in [4]. In that paper the validty of Frostman’s maximum principle for Sario’s potentials was left unsettled. The main object of this paper is to resolve this question (Theorem 1). As a consequence the fundamental theorem of the potential theory is obtained in its complete form for Sario’s potentials (Theorem 2).
Border Reduction in Existence Problems of Harmonic Forms
Authors: Nakai Mitsuru , Sario Leo
Published: July 2016

Given an arbitrary Riemannian n-space V let σ be a harmonic field in the complement V-V0 of a regular region V0. The problem of constructing in v a harmonic field ρ with the property was given a complete solution in [2]. The corresponding problem for harmonic forms σ, ρ remains open iri the general case. In the special case of locally flat spaces the construction can be carried out by replacing by the point norm [3].
Hyperbolic Motions
Authors: Ahlfors Lars V.
Published: July 2016

The observation by Poincaré that Möbius transformations in the complex plane can be lifted to a half-space raises the need to be able to handle motions in hyperbolic space of more than two dimensions by means of an analytic apparatus of not too forbidding complexity. In my experience the best way to do so is to be guided by analogies with the familiar twodimensional case. The purpose of this little paper is to collect a few formulas that the writer has found useful when working with certain hyperbolically invariant operators.
On the Zeros of Power Series with Hadamard Gaps
Authors: Fughs W. H. J.
Published: July 2016

Let

be a power series with Hadamard gaps,

convergent in |z|<1.
Sur les Directions de Julia et de Borel des Fonctions Algebroides
Authors: Toda Nobushige
Published: July 2016

L’extension aux fonctions algébroïdes du théorème de Picard est faite par Rémoundos [7] et après quelques années, celle de la théorie de Nevanlinna aux fonctions algébroïdes dans |z| < + ∞ est donnée par Selberg [9], Ullrich [14] et Valiron [16]. Dans ce mémoire, on considère l’allure des fonctions algébroïdes d’après la méthode dernière.
Adic approximation of complexes, and multiplicities
Authors: Eisenbud David
Published: July 2016

In [2, Section 1.6] Peskine and Szpiro prove a theorem on adic approximations of finite free resolutions over local rings which, together with M. Artin’s Approximation Theorem [1], allows them to “descend” modules of finite projective dimension over the completions of certain local rings to modules of finite projective dimension over finite étale extensions of those rings. In this note we will prove a more general result, which deals with the change in homology under an adic approximation of any complex of finitely generated modules over a noetherian ring, and which allows one to descend not only modules of finite projective dimension, but also the Euler characteristic or intersection multiplicity of two such modules.
Sur le principe du minimum fin
Authors: Nguyen-Xuan-Loc
Published: July 2016

Cet article fait suite à [3c]; dans [3c] étaient étudiées des généralisations éventuelles du principe de minimum fin de Fuglede (voir [2] théo. 9.1. et [3a] théo. 6.) et le cardre était celui des processus de Markov en dualité au sens de Kunita-Watanabe (voir [4b]). Le présent article a le même but, si dans [3c] on a supposé que la limite inférieure fine de la fonction finement hyperharmonique donnée doit être non négative en tout point de la fontière fine de l’ensemble de définition, on se permet dans cet article de supposer que cette lim. inf. fine pourra avoir des valeurs négatives (même égales à — ∞) sur un ensemble polaire de la fontière fine.
Symplectic structures and symmetries of solutions of the complex Monge-Ampére equation
Authors: Einstein-Matthews Stanley M.
Published: July 2016

The graphs that arise from the gradients of solutionsuof the homogeneous complex Monge-Ampère equation are characterized in terms of the natural symplectic structure on the cotangent bundle. This characterization is invariant under symplectic biholomorphisms. Using the symplectic structures we construct symmetries (to be called Lempert transformations) for real valued functionsuwhich are absolutely continuous on lines. We then use these symmetries to generate interesting solutions to the homogeneous complex Monge-Ampère equation and to transform the Poincaré-Lelong equation and the ∂-equation. An example of Lempert transform is given and the main theorem is applied to prove regularity results for exterior nonlinear Dirichlet problem for the homogeneous complex Monge-Ampère equation.
Moduli spaces of stable vector bundles on Enriques surfaces
Authors: Kim Hoil
Published: July 2016

We show that the image of the moduli space of stable bundles on an Enriques surface by the pull back map is a Lagrangian subvariety in the moduli space of stable bundles, which is a symplectic variety, on the covering K3 surface. We also describe singularities and some other features of it.
A general rigidity theorem for complete submanifolds
Authors: Shiohama Katsuhiro , Xu Hongwei
Published: July 2016

Making use of 1-forms and geometric inequalities we prove the rigidity property of complete submanifolds Mn with parallel mean curvature normal in a complete and simply connected Riemannian (n+p) -manifold Nn+p with positive sectional curvature. For given integers n, p and for a nonnegative constant H we find a positive number T(n,p) ∈ (0,1) with the property that if the sectional curvature of N is pinched in [T(n,p), 1], and if the squared norm of the second fundamental form is in a certain interval, then Nn+p is isometric to the standard unit (n + p)-sphere. As a consequence, such an M is congruent to one of the five models as seen in our Main Theorem.
On the Borel summability of divergent solutions of the heat equation
Authors: Lutz D. A. , Miyake M. , Schäfke R.
Published: July 2016

In recent years, the theory of Borel summability or multisummability of divergent power series of one variable has been established and it has been proved that every formal solution of an ordinary differential equation with irregular singular point is multisummable. For partial differential equations the summability problem for divergent solutions has not been studied so well, and in this paper we shall try to develop the Borel summability of divergent solutions of the Cauchy problem of the complex heat equation, since the heat equation is a typical and an important equation where we meet diveregent solutions. In conclusion, the Borel summability of a formal solution is characterized by an analytic continuation property together with its growth condition of Cauchy data to infinity along a stripe domain, and the Borel sum is nothing but the solution given by the integral expression by the heat kernel. We also give new ways to get the heat kernel from the Borel sum by taking a special Cauchy data.
Embeddings of curves and surfaces
Authors: Catanese Fabrizio , Franciosi Marco , Hulek Klaus , Reid Miles
Published: July 2016

We prove a general embedding theorem for Cohen-Macaulay curves (possibly nonreduced), and deduce a cheap proof of the standard results on pluricanonical embeddings of surfaces, assuming vanishing H1(2KX) = 0.
Two meromorphic functions sharing five small functions in the sense of Ēk)(β, f) = Ēk)(β, g)
Authors: Yao Weihong
Published: July 2016

In this paper, we proved a result that if two meromorphic functions f(z) and g(z) share five small functions aj(z) (j = 1,…,5) in the sense of (j = 1,…,5) (k ≥ 22), then we have f(z) ≡ g(z).
On the number of moduli of extendable canonical curves
Authors: Ciliberto Ciro , Lopez Angelo Felice
Published: July 2016

Let C ⊂ ℙg−1 be a canonical curve of genus g. In this article we study the problem of extendability of C, that is when there is a surface S ⊂ ℙg different from a cone and having C as hyperplane section. Using the work of Epema we give a bound on the number of moduli of extendable canonical curves. This for example implies that a family of large dimension of curves that are cover of another curve has general member nonextendable. Using a theorem of Wahl we prove the surjectivity of the Wahl map for the general k-gonal curve of genus g when k = 5, g ≥ 15 or k = 6, g ≥ 13 or k ≥ 7, g ≥ 12.
On classification of ℚ-fano 3-folds of Gorenstein index 2. I
Authors: Takagi Hiromichi
Published: July 2016

We formulate a generalization of K. Takeuchi’s method to classify smooth Fano 3-folds and use it to give a list of numerical possibilities of ℚ-Fano 3-foldsXwith PicX= ℤ(−2KX) andh0(−KX) ≥ 4 containing index 2 pointsPsuch that (X, P) ≃ ({xy+z2+ua= 0}/ℤ2(1, 1, 1, 0),o) for somea∈ ℕ. In particular we prove that then (–KX)3≤ 15 andh0(–KX) ≤ 10. Moreover we show that such anXis birational to a simpler Mori fiber space.
Motivic zeta functions for prehomogeneous vector spaces and castling transformations
Authors: Loeser François
Published: July 2016

We study the behaviour of motivic zeta functions of prehomogeneous vector spaces under castling transformations. In particular we deduce how the motivic Milnor fibre and the Hodge spectrum at the origin behave under such transformations.
Gauss-Manin connection via Witt-Differentials
Authors: Langer Andreas , Zink Thomas
Published: July 2016

Let X/R be a smooth scheme over a ring R. Consider the category of locally free crystals of finite rank on the situs Crys(X/Wt(R)). We show that it is equivalent to the category of locally free -modules of finite rank endowed with a nilpotent, integrable de Rham-Witt connection. In the case where R is a perfect field this was shown by Etesse [E] and Bloch [Bl]. We use the result for a construction of the Gauß-Manin connection as a de Rham-Witt connection.
The 2-Dimensional Calabi Flow
Authors: Chang Shu-Cheng
Published: July 2016

In this paper, based on a Harnack-type estimate and a local Sobolev constant bounded for the Calabi flow on closed surfaces, we extend author’s previous results and show the long-time existence and convergence of solutions of 2-dimensional Calabi flow on closed surfaces. Then we establish the uniformization theorem for closed surfaces.
Algebraic Surfaces of General Type with Small c21 in Positive Characteristic
Authors: Liedtke Christian
Published: July 2016

We establish Noether’s inequality for surfaces of general type in positive characteristic. Then we extend Enriques’ and Horikawa’s classification of surfaces on the Noether line, the so-called Horikawa surfaces. We construct examples for all possible numerical invariants and in arbitrary characteristic, where we need foliations and deformation techniques to handle characteristic 2. Finally, we show that Horikawa surfaces lift to characteristic zero.
Acyclicity of Complexes of Flat Modules
Authors: Hashimoto Mitsuyasu
Published: July 2016

Let R be a noetherian commutative ring, and

a complex of flat R-modules. We prove that if is acyclic for every ρ ϵ Spec R, then is acyclic, and H0() is R-flat. It follows that if is a (possibly unbounded) complex of flat R-modules and is exact for every ρ ϵ Spec R, then is exact for every R-complex . If, moreover, is a complex of projective R-modules, then it is null-homotopic (follows from Neeman’s theorem).
An Invariant Regarding Waring’s Problem for Cubic Polynomials
Authors: Ottaviani Giorgio
Published: July 2016

We compute the equation of the 7-secant variety to the Veronese variety (P4,O(3)), its degree is 15. This is the last missing invariant in the Alexander-Hirschowitz classification. It gives the condition to express a homogeneous cubic polynomial in 5 variables as the sum of 7 cubes (Waring problem). The interesting side in the construction is that it comes from the determinant of a matrix of order 45 with linear entries, which is a cube. The same technique allows to express the classical Aronhold invariant of plane cubics as a pfaffian.
Test Ideals Vs. Multiplier Ideals
Authors: Mustaţă Mircea , Yoshida Ken-Ichi
Published: July 2016

The generalized test ideals introduced in [HY] are related to multiplier ideals via reduction to characteristic p. In addition, they satisfy many of the subtle properties of the multiplier ideals, which in characteristic zero follow via vanishing theorems. In this note we give several examples to emphasize the different behavior of test ideals and multiplier ideals. Our main result is that every ideal in an F-finite regular local ring can be written as a generalized test ideal. We also prove the semicontinuity of F-pure thresholds (though the analogue of the Generic Restriction Theorem for multiplier ideals does not hold).
Presenting cyclotomic q-Schur algebras
Authors: Wada Kentaro
Published: July 2016

We give a presentation of cyclotomicq-Schur algebras by generators and defining relations. As an application, we give an algorithm for computing decomposition numbers of cyclotomicq-Schur algebras.
On the homology of branched coverings of 3-manifolds
Authors: Ueki Jun
Published: July 2016

Following the analogies between 3-manifolds and number rings in arithmetic topology, we study the homology of branched covers of 3-manifolds. In particular, we show some analogues of Iwasawa’s theorems on ideal class groups and unit groups, Hilbert’s Satz 90, and some genus-theory–type results in the context of 3-dimensional topology. We also prove that the 2-cycles valued Tate cohomology of branched Galois covers is a topological invariant, and we give a new insight into the analogy between 2-cycle groups and unit groups.
A dual to tight closure theory
Authors: Epstein Neil , Schwede Karl
Published: July 2016

We introduce an operation on modules over anF-finite ring of characteristicp. We call this operationtight interior. While it exists more generally, in some cases this operation is equivalent to the Matlis dual of tight closure. Moreover, the interior of the ring itself is simply the big test ideal. We directly prove, without appeal to tight closure, results analogous to persistence, colon capturing, and working modulo minimal primes, and we begin to develop a theory dual to phantom homology. Using our dual notion of persistence, we obtain new and interesting transformation rules for tight interiors, and so in particular for the test ideal. Using our theory of phantom homology, we prove a vanishing theorem for maps of Ext. We also compare our theory with Blickle’s notion of Cartier modules, and in the process we prove new existence results for Blickle’s test submodule. Finally, we apply the theory we developed to the study of test ideals in nonnormal rings, proving that the finitistic test ideal coincides with the big test ideal in some cases.
L-functions of p-adic characters
Authors: Davis Christopher , Wan Daqing
Published: July 2016

We define ap-adic character to be a continuous homomorphism fromForp> 2, we use the ring of big Witt vectors overto exhibit a bijection betweenp-adic characters and sequences (ci)(i,p)=1of elements inindexed by natural numbers relatively prime top, and for which. To such ap-adic character we associate anL-function, and we prove that thisL-function isp-adic meromorphic if the corresponding sequence (ci) is overconvergent. If more generally the sequence isClog-convergent, we show that the associatedL-function is meromorphic in the open disk of radiusqC. Finally, we exhibit examples ofClog-convergent sequences with associatedL-functions which are not meromorphic in the disk of radiusqC+∊for any∊> 0.
Generators and Relations for Cyclotomic Units
Authors: Bass Hyman
Published: July 2016

We prove here an unpublished conjecture of Milnor which gives a complete set of multiplicative relations between the numbers

e′(ζ) = 1−ζ,

where ranges over complex roots of unity. Information of this type is useful in certain areas of topology as well as in number theory.
On some Dualities Concerning Abelian Varieties
Authors: Matsumura Hideyuki , Miyanishi Masayoshi
Published: July 2016

The group of extensions Ext(A, Ga) and Ext(A, Gm) of an abelian variety A by the additive or multiplicative group Ga, Gm have been investigated in detail ([9], [10], [GACC]). On the other hand, F. Oort [8] and M. Miyanishi [6] recently studied the groups Ext(Ga, A) and Ext(Gm, A). The purpose of the present paper is to clarify the relationship between these groups. Our results show that the latter groups can be derived from the former.
Cartan Subalgebras of Jordan Algebras
Authors: Jacobson N.
Published: July 2016

In this paper we shall give a definition of an analogue for Jordan algebras of the classical notion of a Cartan subalgebra of a Lie algebra. This is based on a notion of associator nilpotency of a Jordan algebra. A Jordan algebrais called associator nilpotent if there exists a positive (odd) integerMsuch that every associator of orderMformed of elements ofis 0 (§2).
The Cohomology Groups of Tori in Finite Galois Extensions of Number Fields
Authors: Tate J.
Published: July 2016

Class field theory determines in a well-known way the higher dimensional cohomology groups of the idéies and idèle classes in finite Galois extensions of number fields. At the Amsterdam Congress in 1954 I announced [7] the corresponding result for the multiplicative group of the number field itself, but the proof has never been published. Meanwhile, Nakayama showed that results of this type have much broader implications than had been realized. In particular, his theorem allows us to generalize our result from the multiplicative group to the case of an arbitrary torus which is split by the given Galois extension. We also treat the case of “S-units” of the multiplicative group or torus, for a suitably large set of places S. It is a pleasure for me to publish this paper here, in recognition of Nakayama’s important contributions to our knowledge of the cohomological aspects of class field theory; his work both foreshadowed and generalized the theorem under discussion.
The Schur Multipliers of the Mathieu Groups
Authors: Burgoyne N. , Fong P.
Published: July 2016

The Mathieu groups are the finite simple groups M11, M12, M22, M23, M24 given originally as permutation groups on respectively 11, 12, 22, 23, 24 symbols. Their definition can best be found in the work of Witt [1]. Using a concept from Lie group theory we can describe the Schur multiplier of a group as the center of a “simply-connected” covering of that group. A precise definition will be given later. We also mention that the Schur multiplier of a group is the second cohomology group of that group acting trivially on the complex roots of unity. The purpose of this paper is to determine the Schur multipliers of the five Mathieu groups.
Prolongations of G-Structures to Tangent Bundles
Authors: Morimoto Akihiko
Published: July 2016

The purpose of the present paper is to study the prolongations of G-structures on a manifold M to its tangent bundle T(M), G being a Lie subgroup of GL(n,R) with n = dim M. Recently, K. Yano and S. Kobayashi [9] studied the prolongations of tensor fields on M to T(M) and they proposed the following question: Is it possible to associate with each G-structure on M a naturally induced G-structure on T(M), where G′ is a certain subgroup of GL(2n,R)? In this paper we give an answer to this question and we shall show that the prolongations of some special tensor fields by Yano-Kobayashi — for instance, the prolongations of almost complex structures — are derived naturally by our prolongations of the classical G-structures. On the other hand, S. Sasaki [5] studied a prolongation of Riemannian metrics on M to a Riemannian metric on T(M), while the prolongation of a (positive definite) Riemannian metric due to Yano-Kobayashi is always pseudo-Riemannian on T(M) but never Riemannian. We shall clarify the circumstances for this difference and give the reason why the one is positive definite Riemannian and the other is not.
Über Diskontinuierliche Gruppen Picardschen Typus und Zugehörige Eisensteinsche Reihen
Authors: Kubota Tomio
Published: July 2016

Die vorliegènde Arbeit ist eine Zusammenfassung einiger Tatsachen und Formeln betreffs einer Transformationsgruppe, die diskontinuierlich auf dem dreidimensionalen euklidischen Halbraum operiert. Eine solche Gruppe, die zum erstenmal in [5] betrachtet wurde, heiße hier eine diskontinuierliche Gruppe Picardschen Typus. Die in dieser Arbeit angegebenen Resultate ergeben sich grundsätzlich aus der allgemeinen Theorie der algebraischen Gruppen sowie der symmetrischen Räume, und aus der entsprechenden Theorie der Eisensteinschen Reihen. ([1], [2], [4], [6], [7]).
Tensor Product Structure of Affine Demazure Modules and Limit Constructions
Authors: Fourier G. , Littelmann P.
Published: July 2016

Let g be a simple complex Lie algebra, we denote by ĝ the affine Kac-Moody algebra associated to the extended Dynkin diagram of g. Let Λ0 be the fundamental weight of ĝ corresponding to the additional node of the extended Dynkin diagram. For a dominant integral g-coweight λ∨, the Demazure submodule V_λ∨ (mΛ0) is a g-module. We provide a description of the g-module structure as a tensor product of “smaller” Demazure modules. More precisely, for any partition of λ∨ = λ∑j as a sum of dominant integral g-coweights, the Demazure module is (as g-module) isomorphic to ⊗jV_ (mΛ0). For the “smallest” case, λ∨ = ω∨ a fundamental coweight, we provide for g of classical type a decomposition of V_ω∨(mΛ0) into irreducible g-modules, so this can be viewed as a natural generalization of the decomposition formulas in [13] and [16]. A comparison with the Uq(g)-characters of certain finite dimensional -modules (Kirillov-Reshetikhin-modules) suggests furthermore that all quantized Demazure modules V_λ∨,q(mΛ0) can be naturally endowed with the structure of a -module. We prove, in the classical case (and for a lot of non-classical cases), a conjecture by Kashiwara [10], that the “smallest” Demazure modules are, when viewed as g-modules, isomorphic to some KR-modules. For an integral dominant ĝ-weight Λ let V(Λ) be the corresponding irreducible ĝ-representation. Using the tensor product decomposition for Demazure modules, we give a description of the g-module structure of V(Λ) as a semi-infinite tensor product of finite dimensional g-modules. The case of twisted affine Kac-Moody algebras can be treated in the same way, some details are worked out in the last section.
Kazhdan-Lusztig Basis and a Geometric Filtration of an Affine Hecke Algebra
Authors: Tanisaki Toshiyuki , Xi Nanhua
Published: July 2016

According to Kazhdan-Lusztig and Ginzburg, the Hecke algebra of an affine Weyl group is identified with the equivariant K-group of Steinberg’s triple variety. The K-group is equipped with a filtration indexed by closed G-stable subvarieties of the nilpotent variety, where G is the corresponding reductive algebraic group over ℂ. In this paper we will show in the case of type A that the filtration is compatible with the Kazhdan-Lusztig basis of the Hecke algebra.
The monodromy representation and twisted period relations for Appell’s hypergeometric function F 4
Authors: Goto Yoshiaki , Matsumoto Keiji
Published: July 2016

We consider the systemF4(a, b, c)of differential equations annihilating Appell's hypergeometric seriesF4(a,b,c;x). We find the integral representations for four linearly independent solutions expressed by the hypergeometric seriesF4. By using the intersection forms of twisted (co)homology groups associated with them, we provide the monodromy representation ofF4(a, b, c)and the twisted period relations for the fundamental systems of solutions ofF4.
The M-set of λ exp(z)/z has infinite area
Authors: Zhan Guoping , Liao Liangwen
Published: July 2016

It is known that the Fatou set of the map exp(z)/zdefined on the punctured plane ℂ*is empty. We consider theM-set of λ exp(z)/zconsisting of all parameters λ for which the Fatou set of λexp(z)/zis empty. We prove that theM-set of λexp(z)/zhas infinite area. In particular, the Hausdorff dimension of theM-set is 2. We also discuss the area of complement of theM-set.
Weighted sharing and uniqueness of meromorphic functions
Authors: Lahiri Indrajit
Published: July 2016

Introducing the idea of weighted sharing of values we prove some uniqueness theorems for meromorphic functions which improve some existing results.
‘Because of your hardness of heart’: Calvin and the limits of law
Authors: Tuininga Matthew J.
Published: July 2016

This article proposes that Calvin's ‘hardness of heart’ principle functions as a substantive limitation on political authority and the law, creating the legal space for meaningful moral pluralism. Calvin distinguished between the spiritual and civil uses of the law, as well as between the natural moral law and the civil law within the Mosaic law. He repeatedly used Jesus' concept of ‘hardness of heart’ to explain inadequacies within the Mosaic law and to articulate a general principle about the nature and limits of civil law. This approach has important implications for law and morality in contemporary contexts characterised by a degree of moral pluralism that Calvin scarcely could have anticipated.
Shrinking pigeon, brooding dove: the Holy Spirit in recent works by Sarah Coakley and N. T. Wright
Authors: McNall Joshua
Published: July 2016

This article contrasts recent works by Sarah Coakley and N. T. Wright as they pertain to Paul's treatment of the Holy Spirit. In particular, Coakley reveals the inadequacy of Wright's claim that the early fathers were impeded in developing a high view of the Spirit because of an allegiance to ‘Greek philosophy’. Likewise, Wright's more comprehensive treatment of Paul helps to reveal potential problems with Coakley's apophatic tendency to describe the human encounter with God as ‘a love affair with a blank’. In the end, however, both thinkers are united in acknowledging the leading activity of the Spirit, both in prayer and in enabling the Christian to declare that ‘Jesus is Lord’ (1 Cor 12:3). In these ways, both authors converge in an attempt to restore the Holy Spirit to a rightful place in Christian theology and devotion.