bluuebunny/crossref_metadata_2025_split huggingface dataset:
A note on cubic equivalences
Authors: Saito Hiroshi 
Published: July 2016

The present note is intended to be a supplement to [9], in which the following is proven: Let V be a smooth projective variety over the field of complex numbers C, T a smooth quasi-projective variety, Z a cycle in T × V of codimension p. If Z(t) is l-cube equivalent to zero for general t e T, then, setting r = dim V − p,vanishes for l′ < l, where {tZ} is the correspondence defined by Z.
Modules with linear resolution over a polynomial ring in two variables
Authors: Yoshino Yuji 
Published: July 2016

Let k be a field and let S be a polynomial ring k[x1, x2,…, xn] over k in n variables. An S-module M is called a module with linear resolution if M has a free resolution;where, after taking suitable bases of free modules, all fi’s are matrices consisting of linear forms of S. The reader should be referred to Eisenbud- Goto [2, Sections 0 and 1] for elementary facts concerning modules with linear resolution.
Homogeneous line bundles over a toroidal group
Authors: Abe Yukitaka 
Published: July 2016

A connected complex Lie group without non-constant holomorphic functions is called a toroidal group ([5]) or an (H, C)-group ([9]). Let X be an n-dimensional toroidal group. Since a toroidal group is commutative ([5], [9] and [10]), X is isomorphic to the quotient group Cn/Γ by a lattice of Cn. A complex torus is a compact toroidal group. Cousin first studied a non-compact toroidal group ([2]).Let L be a holomorphic line bundle over X. L is said to be homogeneous if is isomorphic to L for all x ε X, where Tx is the translation defined by x ε X. It is well-known that if X is a complex torus, then the following assertions are equivalent:
Correction to “Isospectral surfaces of small genus,” (Nagoya Math. J. Vol. 107 (1987), 13-24)
Authors: Brooks Robert , Tse Richard 
Published: July 2016

It was brought to our attention by Zoran Luicic and Milica Stojanovic, via Peter Gilkey, that some of the diagrams in our paper are not correct.The particular problems are the gluing diagrams for the pair of isospectral surfaces of genus 4, which occur on page 20. It is easy to check that the gluing diagrams given there give rise to a surface of the wrong genus. The problem arose because of carelessness in some of the identifications of some of the edges of the fundamental domain.
On the Transition Probability of a Renewal Process
Authors: Hida Takeyuki 
Published: July 2016

J. L. Doob, D. Blackwell, W. Feller and other authors have obtained several results concerning the renewal theorem. Especially Doob [1] has considered the renewal process and has showed that it becomes a stationary Markov process if we add a certain initial random variable to it. In the present note, we shall study this stationary Markov process and try to determine its transition probability by virtue of a pair of partial differential equations.The author would like to express his hearty thanks to prof. A. Amakusa who has encouraged him with kind discussions throughout the course of preparing the present note.
A Note on Annihilator Relations
Authors: Hinohara Yukitoshi 
Published: July 2016

In a Frobenius algebra A over a field K, there exists a linear function λ of A into K which does not map any proper ideal of A onto 0. Then the map φ : x → xφ where
λ(xy) = λ(yxφ) for all y ε A,defines an automorphism φ of A onto itself. This automorphism is called Nakayama’s automorphism. Now the following result is well known.
The Space of Dirichlet-Finite Solutions of the Equation Δu = Pu on a Riemann Surface
Authors: Nakai Mitsuru 
Published: July 2016

Let R be an open Riemann surface. By a density P on R we mean a non-negative and continuously differentiable functions P(z) of local parameters z = x + iy such that the expression P(z)dxdy is invariant under the change of local parameters z. In this paper we always assume that P≢0 unless the contrary is explicitly mentioned. We consider an elliptic partial differential equationwhich is invariantly defined on R.
The Hessian map in the invariant theory of reflection groups
Authors: Orlik Peter , Solomon Louis 
Published: July 2016

Let V be a complex vector space of dimension l. Let S be the C-algebra of polynomial functions on V. Let Ders be the S-module of derivations of S and let Ωs = Homs (Ders, S) be the dual S-module of differential 1-forms. Let {ei} be a basis for V and let {xi} be the dual basis for V. Then {Di = ∂/∂xi and {dxi} are bases for Ders and Ωs as S-modules. If f ∈ S, define a map Hess (f): Ders → Ωs byThen Hess (f) is an S-module homomorphism which does not depend on the choice of basis for V.
A calculus approach to hyperfunctions III
Authors: Matsuzawa Tadato 
Published: July 2016

In the previous papers, [18] and [19], we have given some basis of a calculus approach to hyperfunctions. We have taken hyperfunctions with the compact support as initial values of the solutions of the heat equation. More precisely, letA′[K]be the space of analytic functionals supported by a compact subsetKofRnand letE(x, t)be then-dimensional heat kernel given by.
Holomorphic mapping into algebraic varieties of general type, II
Authors: Hu Peichu 
Published: July 2016

This announcement is a continuation of Hu [3]. Our results improve Theorem 1 of [3], but the latter is needed in the proof of the former.Let f: M → N be a holomorphic mapping from a connected complex manifold M of dimension m to a projective algebraic manifold N of dimension n.
Young diagrammatic methods in non-commutative invariant theory
Authors: Teranishi Yasuo 
Published: July 2016

In this paper we will study some aspects of non-commutative invariant theory. Let V be a finite-dimensional vector space over a field K of characteristic zero and letK[V] = K⊕V⊕S2(V)⊕…, andK′V› = K⊕V⊕⊕2(V)⊕⊕3V⊕&be respectively the symmetric algebra and the tensor algebra over V. Let G be a subgroup of GL(V). Then G acts on K[V] and K′V›. Much of this paper is devoted to the study of the (non-commutative) invariant ring K′V›G of G acting on K′V›.In the first part of this paper, we shall study the invariant ring in the following situation.
Explicit descriptions of trace rings of generic 2 by 2 matrices
Authors: Teranishi Yasuo 
Published: July 2016

Let K be a field of characteristic zero and letbe m generic n by n matrices over K. That is, xij(k) are independent commuting indeterminates over K. The K-subalgebra generated by X1…, Xm is called a ring of n by n generic matrices and is denoted by R(n, m).
Notes on energy for space-time processes over Lévy processes
Authors: Kanda Mamoru 
Published: July 2016

LetX=(Xt, 0 ≤t< ∞) be a Lévy process on the Euclidean spaceRd, that is, a process onRdwith stationary independent increments which has right continuous paths with left limits. We denote byPxthe probability measure such thatPX(X0= x)= 1 and byExthe expectation relative toPx. The process is characterized by the exponentΨthrough.
The generalized divisor problem and the Riemann hypothesis
Authors: Nakaya Hideki 
Published: July 2016

Let dz(n) be a multiplicative function defined bywhere s = σ + it, z is a. complex number, and ζ(s) is the Riemann zeta function. Here ζz(s) = exp(z log ζ(s)) and let log ζ(s) take real values for real s > 1. We note that if z is a natural number dz(n) coincides with the divisor function appearing in the Dirichlet-Piltz divisor problem, and d-1(n) with the Möbious function.
Ideals of bounded holomorphic functions on simple n-sheeted discs
Authors: Hara Masaru 
Published: July 2016

As usual we denote by H∞(K) the Banach algebra of bounded holomorphic functions on a Riemann surface R equipped with the supremum norm ‖·‖ Consider the ideal I(f1 … fm) of H∞(R) generated by functions f1 …fm in H∞(R). If a function g in H∞(R) belongs to I(f1 … fm or equivalently, if there exist m functions h1 …, hm in H∞(R) withon R, then common zero points of f1, ... fm are also zero points of g in the following strong sense:on R for a positive constant δ > 0. The generalized corona problem asks whether the converse is valid or not. In the case g ≡ 1 on R the problem is referred to simply as the corona problem.
Anisotropic random walks on free products of cyclic groups, irreducible representations and idempotents of C*reg(G)
Authors: Kuhn Gabriella 
Published: July 2016

Let be the free product of q + 1 copies of Zn+1 and let denote its Cayley graph (with respect to aj, 1 ≤ j ≤ q + 1). We may think of G as a group acting on the “homogeneous space” , This point of view is inspired by the case of SL2(R) acting on the hyperbolic disk and is developed in [FT-P] [I-P] [FT-S] [S] (but see also [C]).Since G is a group we may investigate some classical topics: the full (reductive) C* algebra, its dual space, the regular Von Neumann algebra and so on. See [B] [P] [L] [V] and also [H]. These approaches give results pointing up the analogy between harmonic analysis on these groups and harmonic analysis on more classical objects.
Fourier-Eisenstein transform and plancherel formula for rational binary quadratic forms
Authors: Hironaka Yumiko , Sato Fumihiro 
Published: July 2016

Let X be the space of nondegenerate rational symmetric matrices of size 2 and putThe group G acts on X byWe are interested in the space (Γ\X) of Γ-invariant C-valued functions on X and its subspace &(Γ\X) of functions whose supports consist of a finite number of Γ-orbits. The Hecke algebra ℋ(G, Γ) of G with respect to Γ acts naturally on these spaces.
On L-functions associated with the vector space of binary quadratic forms
Authors: Saito Hiroshi 
Published: July 2016

The purpose of this paper is to prove functional equations of L-functions associated with the vector space of binary quadratic forms and determine their poles and residues. For a commutative ring K, let V(K) be the set of all symmetric matrices of degree 2 with coefficients in K. In V(C), we consider the inner productwhere for .
Boundary behaviour of extremal plurisubharmonic functions
Authors: Einstein-Matthews Stanley M. 
Published: July 2016

In [Mo.l], S. Momm studied the boundary behaviour of extremal plurisubharmonic functions by using the pluricomplex Green function gΩ of a bounded convex domain Ω in Cn to exhaust the domain by a family of sublevel sets. Let Ω be a bounded convex domain in Cn containing the origin in its interior. The pluricomplex green function of Ω with a pole
is defined by(1.1)
Riesz capacity and regular boundary points for the parabolic operator of order α
Authors: Nishio Masaharu 
Published: July 2016

Let Rn+1 = Rn × R be the (n + 1)-dimensional Euclidean space with n ≥ 1. We denote by X = (x, t) a point in Rn+1 with x ∈ Rn and t ∈ R. Consider the parabolic operator on Rn+1:where 0 < a ≤ 1 and Δ denotes the Laplacian on Rn.
Limit theorems related to a class of operator-self-similar processes
Authors: Maejima Makoto 
Published: July 2016

An Rd-valued (d ≥ 1) stochastic process X = {X(t)}t≥0 is said to be operator-self-similar if there exists a linear operator D on Rd such that for each c > 0where means the equality for all finite-dimensional distributions and
Finite arithmetic subgroups of GLn, IV
Authors: Kitaoka Yoshiyuki , Suzuki Hiroshi 
Published: July 2016

In this paper, we improve a result of the third paper of this series, that is we showTHEOREM. Let K be a nilpotent extension of the rational number field Q with Galois group Γ, and G a Γ- stable finite subgroup of GLn(0K). Then G is of A-type.
On a Ring Isomorphism Induced by Quasiconformal Mappings
Authors: Nakai Mitsuru 
Published: July 2016

The purpose of this paper is to study the relationship between a certain isomorphism of some rings of functions on Riemann surfaces and a quasi-conformal mapping.It is well known that two compact Hausdorff spaces are topologically equivalent if and only if their rings of continuous functions are isomorphic. We shall establish an analougous result concerning a function ring on a Riemann surface and the quasi-conformal equivalence.
Transforms on white noise functionals with their applications to Cauchy problems
Authors: Chung Dong Myung , Ji Un Cig 
Published: July 2016

AbstractA generalized Laplacian ΔG(K) is defined as a continuous linear operator acting on the space of test white noise functionals. Operator-parameter - and -transforms on white noise functionals are introduced and then prove a characterization theorem for and -transforms in terms of the coordinate differential operator and the coordinate multiplication. As an application, we investigate the existence and uniqueness of solution of the Cauchy problem for the heat equation associated with ΔG(K)
Siegel modular forms and theta series attached to quaternion algebras II
Authors: Böcherer S. , Schulze-Pillot R. 
Published: July 2016

AbstractWe continue our study of Yoshida’s lifting, which associates to a pair of automorphic forms on the adelic multiplicative group of a quaternion algebra a Siegel modular form of degree 2. We consider here the case that the automorphic forms on the quaternion algebra correspond to modular forms of arbitrary even weights and square free levels; in particular we obtain a construction of Siegel modular forms of weight 3 attached to a pair of elliptic modular forms of weights 2 and 4.
On twisting operators and newforms of half-integral weight II – Complete theory of newforms for Kohnen space
Authors: Ueda Masaru 
Published: July 2016

Abstract.The author continues his previous work with the purpose of establishing a theory of newforms in the case of half-integral weight. In this paper, the author formulates and proves a complete theory of newforms for Kohnen space. Kohnen space is an important canonical subspace in the space of cusp forms of half-integral weight k + 1/2 (k > 0). Every Hecke common eigenform in Kohnen space corresponds to a primitive form of integral weight 2k and of odd level via Shimura Correspondence.These newforms for Kohnen space satisfy the Strong multiplicity One theorem. Moreover, we explicitly determine the corresponding primitive form (of weight 2k) to each newform for Kohnen space. The space of oldforms is also explicitly described.In order to find all newforms for Kohnen space, the author needs a certain non-vanishing property of Fourier coefficients of cusp forms. Such property proves by using representation theory of finite linear groups. The method of proof of newform theory is mainly based on trace formulae and trace relations.
Transformations on white noise functions associated with second order differential operators of diagonal type
Authors: Chung Dong Myung , Ji Un Cig , Obata Nobuaki 
Published: July 2016

Abstract.A generalized number operator and a generalized Gross Laplacian are introduced on the basis of white noise distribution theory. The equicontinuity is examined and associated one-parameter transformation groups are constructed. An infinite dimensional analogue of ax + b group and Cauchy problems on white noise space are discussed.
Tensor products of matrix factorizations
Authors: Yoshino Yuji 
Published: July 2016

Abstract.Let K be a field and let f ∈ K[[x1, x2,…,xr]] and g ∈ K[[y1, y2,…,ys]] be non-zero and non-invertible elements. If X (resp. Y) is a matrix factorization of f (resp. g), then we can construct the matrix factorization X ⊗̂ Y of f + g over K[[x1, x2,…,xr, y1, y2,…,ys]], which we call the tensor product of X and Y.After showing several general properties of tensor products, we will prove theorems which give bounds for the number of indecomposable components in the direct decomposition of X ⊗̂ Y.
Extension of CR structures on three dimensional pseudoconvex CR manifolds
Authors: Cho Sanghyun 
Published: July 2016

Abstract.Letbe a smoothly bounded orientable pseudoconvexCRmanifold of finite type anddimℝM= 3. Then we extend the givenCRstructure onMto an integrable almost complex structure onwhich is the concave side ofMandM⊂
Very ampleness of adjoint linear systems on smooth surfaces with boundary
Authors: Maşek Vladimir 
Published: July 2016

AbstractLet M be a ℚ-divisor on a smooth surface over ℂ. In this paper we give criteria for very ampleness of the adjoint of [M], the round-up of M. (Similar results for global generation were given by Ein and Lazarsfeld and used in their proof of Fujita’s Conjecture in dimension 3.) In §4 we discuss an example which suggests that this kind of criteria might also be useful in the study of linear systems on surfaces.
Z-graduations de type parabolique et polynomes harmoniques
Authors: Mortajine Abdel Latif 
Published: July 2016

AbstractWe give pluriharmonic and harmonic representations of prehomogeneous vector spaces of regular classical parabolic type (L = Γ×M, V) througt the commutative quotients V ‖ M = spec(C[V]M) of them.
Hilbert-Asai Eisenstein series, regularized products, and heat kernels
Authors: Jorgenson Jay , Lang Serge 
Published: July 2016

AbstractIn a famous paper, Asai indicated how to develop a theory of Eisenstein series for arbitrary number fields, using hyperbolic 3-space to take care of the complex places. Unfortunately he limited himself to class number 1. The present paper gives a detailed exposition of the general case, to be used for many applications. First, it is shown that the Eisenstein series satisfy the authors’ definition of regularized products satisfying the generalized Lerch formula, and the basic axioms which allow the systematic development of the authors’ theory, including the Cramér theorem. It is indicated how previous results of Efrat and Zograf for the strict Hilbert modular case extend to arbitrary number fields, for instance a spectral decomposition of the heat kernel periodized with respect to SL2 of the integers of the number field. This gives rise to a theta inversion formula, to which the authors’ Gauss transform can be applied. In addition, the Eisenstein series can be twisted with the heat kernel, thus encoding an infinite amount of spectral information in one item coming from heat Eisenstein series. The main expected spectral formula is stated, but a complete exposition would require a substantial amount of space, and is currently under consideration.
Uniqueness problem with truncated multiplicities in value distribution theory, II
Authors: Fujimoto Hirotaka 
Published: July 2016

AbstractLet H1, H2,…,Hq be hyperplanes in PN (ℂ) in general position. Previously, the author proved that, in the case where q ≥ 2N + 3, the condition ν(f,Hj) = ν(g, Hj) imply f = g for algebraically nondegenerate meromorphic maps f, g: ℂn → PN(ℂ), where ν(f, Hj) denote the pull-backs of Hj through f considered as divisors. In this connection, it is shown that, for q ≥ 2N + 2, there is some integer ℓ0 such that, for any two nondegenerate meromorphic maps f, g: ℂn → PN(ℂ) with min(ν(f, Hj),ℓ0) = min(ν(g, Hj), ℓ0) the map f × g into PN(ℂ) × PN(ℂ) is algebraically degenerate. He also shows that, for N = 2 and q = 7, there is some ℓ0 such that the conditions min(ν(f, Hj), ℓ0) = min(ν(g, Hj), ℓ0) imply f = g for any two nondegenerate meromorphic maps f, g into P2(ℂ) and seven generic hyperplanes Hj’s.
On the classification of 3-dimensionalSL2(ℂ)-varieties
Authors: Kebekus Stefan 
Published: July 2016

In the present work we describe 3-dimensional complexSL2-varieties where the genericSL2-orbit is a surface. We apply this result to classify the minimal 3-dimensional projective varieties with Picard-number 1 where a semisimple group acts such that the generic orbits are 2-dimensional.This is an ingredient of the classification [Keb99] of the 3-dimensional relatively minimal quasihomogeneous varieties where the automorphism group is not solvable.
On the Ring of Integers in an Algebraic Number Field as a representation Module of Galois Group
Authors: Yokoi Hideo 
Published: July 2016

1. Introduction. It is known that there are only three rationally inequivalent classes of indecomposable integral representations of a cyclic group of prime order l. The representations of these classes are:
(I) identical representation,(II) rationally irreducible representation of degree l – 1,(III) indecomposable representation consisting of one identical representation and one rationally irreducible representation of degree l-1 (F. E. Diederichsen [1], I. Reiner [2]).
On the Auslander-Reiten quiver of an infinitesimal group
Authors: Farnsteiner Rolf 
Published: July 2016

AbstractLetbe an infinitesimal group scheme, defined over an algebraically closed field of characteristic p. We employ rank varieties of-modules to study the stable Auslander-Reiten quiver of the distribution algebra of. As in case of finite groups, the tree classes of the AR-components are finite or infinite Dynkin diagrams, or Euclidean diagrams. We classify the components of finite and Euclidean type in caseis supersolvable or a Frobenius kernel of a smooth, reductive group.
On the unramified common divisor of discriminants of integers in a normal extension
Authors: Oka Satomi 
Published: July 2016

AbstractLet F be an algebraic number field of a finite degree, and K be a normal extension over F of a finite degree n. Let be a prime ideal of F which is unramified in K/F, be a prime ideal of K dividing such that . Denote by δ(K/F) the greatest common divisor of discriminants of integers of K with respect to K/F. Then, divides δ(K/F) if and only if
The moduli space of bilevel-6 abelian surfaces
Authors: Sankaran G. K. , Spandaw J. G. 
Published: July 2016

AbstractWe show that the moduli space of abelian surfaces with polarisation of type (1,6) and a bilevel structure has positive Kodaira dimension and indeed pg ≥ 3. To do this we show that three of the Siegel cusp forms with character for the paramodular symplectic group constructed by Gritsenko and Nikulin are cusp forms without character for the modular group associated to this moduli problem. We then calculate the divisors of the corresponding differential forms, using information about the fixed loci of elements of the paramodular group previously obtained by Brasch.
Multiplier Hermitian structures on Kähler manifolds
Authors: Mabuchi Toshiki 
Published: July 2016

AbstractThe main purpose of this paper is to make a systematic study of a special type of conformally Kähler manifolds, called multiplier Hermitian manifolds, which we often encounter in the study of Hamiltonian holomorphic group actions on Kähler manifolds. In particular, we obtain a multiplier Hermitian analogue of Myers’ Theorem on diameter bounds with an application (see [M5]) to the uniquness up to biholomorphisms of the “Kähler-Einstein metrics” in the sense of [M1] on a given Fano manifold with nonvanishing Futaki character.
A combinatorial identity for the derivative of a theta series of a finite type root lattice
Authors: Naito Satoshi 
Published: July 2016

AbstractLet be a (not necessarily simply laced) finite-dimensional complex simple Lie algebra with the Cartan subalgebra and Q ⊂ * the root lattice. Denote by ΘQ(q) the theta series of the root lattice Q of . We prove a curious “combinatorial” identity for the derivative of ΘQ(q), i.e. for by using the representation theory of an affine Lie algebra.
Algebro-geometric version of Nevanlinna’s lemma on logarithmic derivative and applications
Authors: Yamanoi Katsutoshi 
Published: July 2016

AbstractIn this paper we shall establish some generalization of Nevanlinna’s Lemma on Logarithmic Derivative to the case of meromorphic maps from a finite analytic covering space over the m-dimensional complex affine space ℂm to a smooth complex projective variety. Then we shall apply this to “the Second Main Theorem” in Nevanlinna theory in several complex variables.