bluuebunny/crossref_metadata_2025_split huggingface dataset:
The dimension formula of the space of cusp forms of weight one for Γ0(p)
Authors: Tanigawa Yoshio , Ishikawa Hirofumi 
Published: July 2016

The purpose of this paper is to study the dimension formula for cusp forms of weight one, following the series of Hiramatsu [2] and Hiramatsu-Akiyama [3]. We define as usual the subgroup Γ0(N) of SL2(Z) by.
Polynomial rings and their projective modules
Authors: Popescu Dorin 
Published: July 2016

Let R be a regular noetherian ring. A central question concerning projective modules over polynomial R-algebras is the following.(1.1) BASS-QUILLEN CONJECTURE ([2] Problem IX, [10]). Every finitely generated projective module P over a polynomial R-algebra R[T], T = (T1,…, Tn) is extended from R, i.e.P≊R[T]⊗R P/(T)P.
The volumes of small geodesic balls and generalized Chern numbers of Kaehler manifolds
Authors: Blazic Novica 
Published: July 2016

In this paper we study a connection between global and local properties of Kaehler manifolds, more specifically we study a connection between the volumes of small geodesic balls of a manifold M and some generalized Chern numbers. We use the standard power series expansion for Vm(r).In Theorem 3.1 we give characterizations of a flat compact Kaehler manifold in terms of the volumes of small geodesic balls and generalized Chern numbers ωn-1c1(M) and ωn-2c12(M). In Theorem 4.1 similar questions for complex space forms are considered. So we prove one particular case of the Conjecture (IV) stated by Gray and Vanhecke [6].
On the Dimension of Modules and Algebras, V. Dimension of Residue Rings
Authors: Eilenberg Samuel , Nakayama Tadasi 
Published: July 2016

We shall consider a semi-primary ring ۸ with radical N (i.e. N is nilpotent and ۸/N is semi-simple (with minimum condition)). All modules considered are left ۸-modules. We refer to [1] for all notions relevant to homological algebra.The objective of this paper is to establish the following two theorems:Theorem I. Let a be a two-sided ideal in A such that
The law of the iterated logarithm on subsequences-characterizations
Authors: Weber Michel 
Published: July 2016

Let be any increasing sequence of integers and M> 1; we connect to them in a very simply way, an increasing unbounded function φ: → R+. Let also X1, X2, · · · be a sequence of i.i.d. random vectors with value in euclidian space Rm. We prove that the cluster set of the sequence almost surely coincides with the unit ball of Rm, if, and only if, the covariance matrix of X1 is the identity matrix of Rm and EX1 is the zero vector of Rm. We define a functional A on the set of increasing sequences of integers as follows:.
Super congruence for the Apéry numbers
Authors: Ishikawa Tsuneo 
Published: July 2016

Let, for any n ≥ 0,.R. Apéry’s proof of the irrationality of ζ(2) and ζ(3) made use of these numbers (see [10]). As a result, many properties of the Apéry numbers were found (see [l]-[9]). In particular, Beukers and Stienstra showed the interesting congruence (see [11, Theorem 13.1]).
On the least degree of polynomials bounding above the differences between lengths and multiplicities of certain systems of parameters in local rings
Authors: Cuong Nguyen Tu 
Published: July 2016

Let A be a commutative local Noetherian ring with the maximal ideal m and M a finitely generated A-module, d = dim M. It is well-known that the difference between the length and the multiplicity of a parameter ideal q of Mgives a lot of informations on the structure of the module M. For instance, M is a Cohen-Macaulay (CM for short) module if and only if IM(q) = 0 for some parameter ideal q or M is Buchsbaum module (see [S-V]) if and only if IM(q) is a constant for all parameter ideals q of M.
Holomorphic families of geodesic discs in infinite dimensional Teichmüller spaces
Authors: Tanigawa Harumi 
Published: July 2016

The theory of quasiconformal mappings plays an important role in Teichmüller theory. The Teichmüller spaces of Riemann surfaces are defined as quotient spaces of the spaces of Beltrami differentials, and the Teichmüller distances are defined to measure quasiconformal deformations between the Riemann surfaces representing points in the Teichmüller spaces. The Teichmüller spaces are complex Banach manifolds equipped with natural complex structures such that the canonical projections are holomorphic. It is known (see Gardinar [4]) that the Teichmüller distance, defined independently of the complex structures, coincides with the Kobayashi distance.In spite of the naturality of the definition of a Teichmüller space as a quotient of Beltrami differentials, for given two Beltrami differentials it is hard to determine whether they are equivalent or not. For this reason, it is not trivial to describe geodesic lines with respect to the Teichmüller-Kobayashi metric.
On subclasses of infinitely divisible distributions on R related to hitting time distributions of 1-dimensional generalized diffusion processes
Authors: Yamazato Makoto 
Published: July 2016

A distribution μ on R+ = [0, ∞) is said to be a distribution if there are an increasing (in the strict sense) sequence of positive real numbers such that, for each j = 0, …, m, there is at least one ak satisfying bj < ak < b+1 and theLaplace transform of μ is represented as
Newton polygons and gevrey indices for linear partial differential operators
Authors: Miyake Masatake , Hashimoto Yoshiaki 
Published: July 2016

This paper is a continuation of Miyake [7] by the first named author. We shall study the unique solvability of an integro-differential equation in the category of formal or convergent power series with Gevrey estimate for the coefficients, and our results give some analogue in partial differential equations to Ramis [10, 11] in ordinary differential equations.In the study of analytic ordinary differential equations, the notion of irregularity was first introduced by Malgrange [3] as a difference of indices of a differential operator in the categories of formal power series and convergent power series. After that, Ramis extended his theory to the category of formal or convergent power series with Gevrey estimate for the coefficients. In these studies, Ramis revealed a significant meaning of a Newton polygon associated with a differential operator.
Estimates for fourier coefficients of siegel cusp forms of degree two, II
Authors: Kohnen Winfried 
Published: July 2016

Let F be a Siegel cusp form of integral weight k on Γ2: = Sp2(Z) and denote by a(T) (T a positive definite symmetric half-integral (2,2)-matrix) its Fourier coefficients. In [2] Kitaoka proved that(1)(the result is actually stated only under the assumption that k is even). In our previous paper [3] it was shown that one can attain(2)
Minorations d’unités fondamentales—applications
Authors: Louboutin Stéphane 
Published: July 2016

Un idéal entierId’un corps quadratique réelkest ditprimitiflorsquen∈ N* et (n) diviseIimpliquentn =1. Un idéal entier est primitif si et seulement si il vérifie les trois conditions suivantes:(i) il n’est divisible par aucun idéal premier inerte,(ii) il n’est divisible par le carré d’aucun idéal premier ramifié,(iii) si il est divisible par un idéal premier totalement décomposé, alors il n’est pas divisible par son idéal premier conjugué.
A note on the Følner condition for amenability
Authors: Adachi Toshiaki 
Published: July 2016

Let G be a countably generated discrete group. A right-invariant mean μ on G is a bounded linear functional of the space L∞(G) of bounded functions on G having the property:We say that G is amenable if it is equipped with a right-invariant mean. Finite groups, abelian groups, in fact, groups of subexponential growth are amenable. Solvable group are also amenable. Subgroups and quotients of amenable groups are amenable. On the other hand, free groups having two generators and over are non-amenable.
On Real Irreducible Representations of Lie Algebras
Authors: Iwahori Nagayoshi 
Published: July 2016

Let us consider the following two problems:Problem A. Let g be a given Lie algebra over the real number field R. Then find all real, irreducible representations of g.Problem B. Let n be a given positive integer. Then find all irreducible subalgebras of the Lie algebra ôí(w, R) of all real matrices of degree n.
Discrete spectrum of many body Schrödinger operators with non-constant magnetic fields I
Authors: Hattori Tetsuya 
Published: July 2016

In this paper we discuss the discrete spectrum of the Schrödinger operatorHNZ(b), defined as below, for an atomic system in a magnetic field. Letwherexjis a point inR3(1≥ j ≥ N), and∇jbe the gradient inR3with respect toxj(1 ≥ j ≥ N). Then we consider the following operator:(1.1)defined on, where3 being real-valued and(1.2)
On Barth’s conjecture concerining
Authors: Coltoiu Mihnea 
Published: July 2016

A classical, still unsolved problem, is the following: is every connected curve A ⊂ P3 a set-theoretic complete intersection? It is clear that if A is a set-theoretic complete intersection then:a) The algebraic cohomology groups vanish for every coherent algebraic sheaf on P3.b) The analytic cohomology groups vanish for every coherent analytic sheaf on P3\A.
On zeta functions associated to symmetric matrices III – An explicit form of L-Functions
Authors: Ibukiyama Tomoyoshi , Saito Hiroshi 
Published: July 2016

Abstract.In [I-S2], we gave an explicit form of zeta functions associated to the space of symmetric matrices. In this paper, the case of L-functions is treated. In the case of definite symmetric matrices, we show the ratinality of special values of these L-functions.
Symmetries in the fourth Painlevé equation and Okamoto polynomials
Authors: Noumi Masatoshi , Yamada Yasuhiko 
Published: July 2016

AbstractThe fourth Painlevé equation PIV is known to have symmetry of the affine Weyl group of type with respect to the Bäcklund transformations. We introduce a new representation of PIV, called the symmetric form, by taking the three fundamental invariant divisors as the dependent variables. A complete description of the symmetry of PIV is given in terms of this representation. Through the symmetric form, it turns out that PIV is obtained as a similarity reduction of the 3-reduced modified KP hierarchy. It is proved in particular that the special polynomials for rational solutions PIV, called Okamoto polynomials, are expressible in terms of the 3-reduced Schur functions.
Magnetic scattering at low energy in two dimensions
Authors: Tamura Hideo 
Published: July 2016

AbstractWe study the asymptotic behavior at low energy of scattering amplitudes in two dimensional magnetic fields with compact support. The obtained result depends on the total flux of magnetic fields. It should be noted that magnetic potentials do not necessarily fall off rapidly at infinity. The main body of argument is occupied by the resolvent analysis at low energy for magnetic Schrödinger operators with perturbations of lang-range class. We can show that the dimension of resonance spaces at zero energy does not exceed two. As a simple application, we also discuss the scattering by magnetic field with small support and the convergence to the scattering amplitude by δ-like magnetic field.
A remark on algebraic surfaces with polyhedral Mori cone
Authors: Nikulin Viacheslav V. 
Published: July 2016

We denote by FPMC the class of all non-singular projective algebraic surfaces X over ℂ with finite polyhedral Mori cone NE(X) ⊂ NS(X) ⊗ ℝ. If ρ(X) = rk NS(X) ≥ 3, then the set Exc(X) of all exceptional curves on X ∈ FPMC is finite and generates NE(X). Let δE(X) be the maximum of (-C2) and pE(X) the maximum of pa(C) respectively for all C ∈ Exc(X). For fixed ρ ≥ 3, δE and pE we denote by FPMCρ,δE,pE the class of all algebraic surfaces X ∈ FPMC such that ρ(X) = ρ, δE(X) = δE and pE(X) = pE. We prove that the class FPMCρ,δE,pE is bounded in the following sense: for any X ∈ FPMCρ,δE,pE there exist an ample effective divisor h and a very ample divisor h′ such that h2 ≤ N(ρ, δE) and h′2 ≤ N′(ρ, δE, pE) where the constants N(ρ, δE) and N′(ρ, δE, pE) depend only on ρ, δE and ρ, δE, pE respectively.One can consider Theory of surfaces X ∈ FPMC as Algebraic Geometry analog of the Theory of arithmetic reflection groups in hyperbolic spaces.
Affine structure on Weil bundles
Authors: Kolář Ivan 
Published: July 2016

AbstractFor every r-th order Weil functor TA, we introduce the underlying k-th order Weil functors We deduce that is an affine bundle for every manifold M. Generalizing the classical concept of contact element by C. Ehresmann, we define the bundle of contact elements of type A on M and we describe some affine properties of this bundle.
On the Steinitz module and capitulation of ideals
Authors: Khare Chandrashekhar , Prasad Dipendra 
Published: July 2016

AbstractLet L be a finite extension of a number field K with ring of integers and respectively. One can consider as a projective module over . The highest exterior power of as an module gives an element of the class group of , called the Steinitz module. These considerations work also for algebraic curves where we prove that for a finite unramified cover Y of an algebraic curve X, the Steinitz module as an element of the Picard group of X is the sum of the line bundles on X which become trivial when pulled back to Y. We give some examples to show that this kind of result is not true for number fields. We also make some remarks on the capitulation problem for both number field and function fields. (An ideal in is said to capitulate in L if its extension to is a principal ideal.)
On the deduction of the class field theory from the general reciprocity of power residues
Authors: Kubota Tomio , Oka Satomi 
Published: July 2016

AbstractWe denote by (A) Artin’s reciprocity law for a general abelian extension of a finite degree over an algebraic number field of a finite degree, and denote two special cases of (A) as follows: by (AC) the assertion (A) where K/F is a cyclotomic extension; by (AK) the assertion (A) where K/F is a Kummer extension. We will show that (A) is derived from (AC) and (AK) only by routine, elementarily algebraic arguments provided that n = (K : F) is odd. If n is even, then some more advanced tools like Proposition 2 are necessary. This proposition is a consequence of Hasse’s norm theorem for a quadratic extension of an algebraic number field, but weaker than the latter.
Hilbert-Kunz Multiplicity of Two-Dimensional Local Rings
Authors: Watanabe Kei-Ichi , Yoshida Ken-Ichi 
Published: July 2016

We study the behavior of Hilbert-Kunz multiplicity for powers of an ideal, especially the case of stable ideals and ideals in local rings of dimension 2. We can characterize regular local rings by certain equality between Hilbert-Kunz multiplicity and usual multiplicity.We show that rings with “minimal” Hilbert-Kunz multiplicity relative to usual multiplicity are “Veronese subrings” in dimension 2.
Oscillation results for n-th order linear differential equations with meromorphic periodic coefficients
Authors: Shimomura Shun 
Published: July 2016

AbstractConsider n-th order linear differential equations with meromorphic periodic coefficients of the form w(n) + Rn-1(ez)w(n-1) + … + R1(ez)w′ + R0(ez)w = 0, n ≥ 2, where Rv(t) (0 ≤ ν ≤ n – 1) are rational functions of t. Under certain assumptions, we prove oscillation theorems concerning meromorphic solutions, which contain necessary conditions for the existence of a meromorphic solution with finite exponent of convergence of the zero-sequence. We also discuss meromorphic or entire solutions whose zero-sequences have an infinite exponent of convergence, and give a new zero-density estimate for such solutions.
Monogenesis of the rings of integers in certain imaginary abelian fields
Authors: Shah Syed Inayat Ali , Nakahara Toru 
Published: July 2016

AbstractIn this paper we consider a subfield K in a cyclotomic field km of conductor m such that [km: K] = 2 in the cases of m = lpn with a prime p, where l = 4 or p > l = 3. Then the theme is to know whether the ring of integers in K has a power basis or does not.
Special rays in the Mori cone of a projective variety
Authors: Andreatta Marco , Occhetta Gianluca 
Published: July 2016

AbstractLet X be a smooth n-dimensional projective variety over an algebraically closed field k such that KX is not nef. We give a characterization of non nef extremal rays of X of maximal length (i.e of length n – 1); in the case of Char(k) = 0 we also characterize non nef rays of length n – 2.
Convergence of the zeta functions of prehomogeneous vector spaces
Authors: Saito Hiroshi 
Published: July 2016

AbstractLet (G, ρ, X) be a prehomogeneous vector space with singular set S over an algebraic number field F. The main result of this paper is a proof for the convergence of the zeta fucntions Z(Φ, s) associated with (G, ρ, X) for large Re s under the assumption that S is a hypersurface. This condition is satisfied if G is reductive and (G, ρ, X) is regular. When the connected component of the stabilizer of a generic point x is semisimple and the group Πx of connected components of Gx is abelian, a clear estimate of the domain of convergence is given.Moreover when S is a hypersurface and the Hasse principle holds for G, it is shown that the zeta fucntions are sums of (usually infinite) Euler products, the local components of which are orbital local zeta functions. This result has been proved in a previous paper by the author under the more restrictive condition that (G, ρ, X) is irreducible, regular, and reduced, and the zeta function is absolutely convergent.
On uniqueness polynomials for meromorphic functions
Authors: Fujimoto Hirotaka 
Published: July 2016

AbstractA polynomialP(w)is called a uniqueness polynomial (or a uiqueness polynomial in a broad sense) ifP(f) = cP(g)(orP(f) = P(g))impliesf=gfor any nonzero constantcand nonconstant meromorphic functionsfandgonC. We consider a monic polynomialP(w)without multiple zero whose derivative has mutually distinctkzerosejwith multiplicitiesqj.Under the assumption thatP(el) ≠ P(em)for all distinctlandm,we prove thatP(w)is a uniqueness polynomial in a broad sense if and only if ∑l<mqlqm> ∑lql. We also give some sufficient conditions for uniqueness polynomials.
Application of theτ-function theory of Painlevé equations to random matrices:PVI, the JUE, CyUE, cJUE and scaled limits
Authors: Forrester P. J. , Witte N. S. 
Published: July 2016

AbstractOkamoto has obtained a sequence ofτ-functions for the PVIsystem expressed as a double Wronskian determinant based on a solution of the Gauss hypergeometric equation. Starting with integral solutions of the Gauss hypergeometric equation, we show that the determinant can be re-expressed as multidimensional integrals, and these in turn can be identified with averages over the eigenvalue probability density function for the Jacobi unitary ensemble (JUE), and the Cauchy unitary ensemble (CyUE) (the latter being equivalent to the circular Jacobi unitary ensemble (cJUE)). Hence these averages, which depend on four continuous parameters and the discrete parameterN, can be characterised as the solution of the second order second degree equation satisfied by the Hamiltonian in the PVItheory. We show that the Hamiltonian also satisfies an equation related to the discrete PVequation, thus providing an alternative characterisation in terms of a difference equation. In the case of the cJUE, the spectrum singularity scaled limit is considered, and the evaluation of a certain four parameter average is given in terms of the general PVtranscendent inσform. Applications are given to the evaluation of the spacing distribution for the circular unitary ensemble (CUE) and its scaled counterpart, giving formulas more succinct than those known previously; to expressions for the hard edge gap probability in the scaled Laguerre orthogonal ensemble (LOE) (parameteraa non-negative integer) and Laguerre symplectic ensemble (LSE) (parameteraan even non-negative integer) as finite dimensional combinatorial integrals over the symplectic and orthogonal groups respectively; to the evaluation of the cumulative distribution function for the last passage time in certain models of directed percolation; to theτ-function evaluation of the largest eigenvalue in the finite LOE and LSE with parametera =0; and to the characterisation of the diagonal-diagonal spin-spin correlation in the two-dimensional Ising model.
Solutions in Morrey spaces of some semilinear heat equations with time-dependent external forces
Authors: Zhou Xiaofang 
Published: July 2016

AbstractIn this paper, we consider the Cauchy problem for some semilinear heat equations with time-dependent external forces. Both the external force and the initial data are assumed to be small in some Morrey spaces. We first prove the unique existence of a small time-global solution. We next show the stability of that solution by proving the time-global sovability of perturbation problems.
Wiman-Valiron method for difference equations
Authors: Ishizaki K. , Yanagihara N. 
Published: July 2016

AbstractLet f(z) be an entire function of order less than 1/2. We consider an analogue of the Wiman-Valiron theory rewriting power series of f(z) into binomial series. As an application, it is shown that if a transcendental entire solution f(z) of a linear difference equation is of order χ < 1/2, then we have log M (r, f) = Lrχ(1 + o(1)) with a constant L > 0.
Formation and construction of a shock wave for 3-D compressible Euler equations with the spherical initial data
Authors: Yin Huicheng 
Published: July 2016

AbstractIn this paper, the problem on formation and construction of a shock wave for three dimensional compressible Euler equations with the small perturbed spherical initial data is studied. If the given smooth initial data satisfy certain nondegeneracy conditions, then from the results in [22], we know that there exists a unique blowup point at the blowup time such that the first order derivatives of a smooth solution blow up, while the solution itself is still continuous at the blowup point. From the blowup point, we construct a weak entropy solution which is not uniformly Lipschitz continuous on two sides of a shock curve. Moreover the strength of the constructed shock is zero at the blowup point and then gradually increases. Additionally, some detailed and precise estimates on the solution are obtained in a neighbourhood of the blowup point.
On Elliptic Curves in SL2(ℂ)/Γ.., Schanuel’s Conjecture and Geodesic Lengths
Authors: Winkelmann Jörg 
Published: July 2016

AbstractLet Γ be a discrete cocompact subgroup of SL2(ℂ). We conjecture that the quotient manifold X = SL2(ℂ) / Γ contains infinitely many non-isogenous elliptic curves and prove this is indeed the case if Schanuel’s conjecture holds. We also prove it in the special case where Γ ∩ SL2(∝) is cocompact in SL2(ℝ).Furthermore, we deduce some consequences for the geodesic length spectra of real hyperbolic 2- and 3-folds.
The Theorem of Bo Chen and Hall Polynomials
Authors: Ringel Claus Michael 
Published: July 2016

AbstractLet Λ be the path algebra of a Dynkin quiver. A recent result of Bo Chen asserts that Hom(X; Y/X) = 0 for any Gabriel-Roiter inclusion X ⊆ Y. The aim of the present note is to give an interpretation of this result in terms of Hall polynomials, and to extend it in this way to representation-directed split algebras. We further show its relevance when dealing with arbitrary representation-finite split algebras.