FullText URL mjou_064_001_011.pdf
Author Hoshi, Yuichiro|
Abstract In the present paper, we consider torsion points on ample divisors on abelian varieties. We prove that, for each integer n ≤ 2, an effective divisor of level n on an abelian variety does not contain the subgroup of n-torsion points. Moreover, we also discuss an application of this result to the study of the p-rank of cyclic coverings of curves in positive characteristic.
Keywords abelian variety torsion point curve p-rank
Published Date 2022-01
Publication Title Mathematical Journal of Okayama University
Volume volume64
Issue issue1
Publisher Department of Mathematics, Faculty of Science, Okayama University
Start Page 1
End Page 11
ISSN 0030-1566
NCID AA00723502
Content Type Journal Article
language 英語
Copyright Holders Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
FullText URL mjou_064_075_107.pdf
Author Nagamachi, Ippei|
Abstract We give good reduction criteria for hyperbolic polycurves, i.e., successive extensions of families of curves, under some assumptions. These criteria are higher dimensional versions of the good reduction criterion for hyperbolic curves given by Oda and Tamagawa.
Keywords good reduction, hyperbolic curve, polyucurve, ètale fundamental group.
Published Date 2022-01
Publication Title Mathematical Journal of Okayama University
Volume volume64
Issue issue1
Publisher Department of Mathematics, Faculty of Science, Okayama University
Start Page 75
End Page 107
ISSN 0030-1566
NCID AA00723502
Content Type Journal Article
language 英語
Copyright Holders Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
FullText URL mjou_064_031_045.pdf
Author Yamagishi, Hiroyuki|
Abstract We have the best constants of three kinds of discrete Sobolev inequalities on the complete bipartite graph with 2N vertices, that is, K<sub>N</sub>,<sub>N</sub>. We introduce a discrete Laplacian A on K<sub>N</sub>,<sub>N</sub>. A is a 2N ×2N real symmetric positive-semidefinite matrix whose eigenvector corresponding to zero eigenvalue is 1 = <sup>t</sup>(1, 1, … , 1)&isin; C<sup>2N</sup>. A discrete heat kernel, a Green’s matrix and a pseudo Green’s matrix play important roles in giving the best constants.
Keywords Discrete Sobolev inequality Discrete Laplacian Green’s matrix Reproducing relation
Published Date 2022-01
Publication Title Mathematical Journal of Okayama University
Volume volume64
Issue issue1
Publisher Department of Mathematics, Faculty of Science, Okayama University
Start Page 31
End Page 45
ISSN 0030-1566
NCID AA00723502
Content Type Journal Article
language 英語
Copyright Holders Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
FullText URL mjou_064_063_073.pdf
Author Tasaka, Koji|
Abstract A partial answer to a conjecture about the rank of the matrix C<sub>N</sub>,<sub>r</sub> introduced by Francis Brown in the study of totally odd multiple zeta values is given.
Keywords Multiple zeta values Period polynomials
Published Date 2022-01
Publication Title Mathematical Journal of Okayama University
Volume volume64
Issue issue1
Publisher Department of Mathematics, Faculty of Science, Okayama University
Start Page 63
End Page 73
ISSN 0030-1566
NCID AA00723502
Content Type Journal Article
language 英語
Copyright Holders Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
FullText URL mjou_064_191_213.pdf
Author Suzuki, Takeshi| Toyosawa, Yoshitaka|
Abstract We present a conjectural hook formula concerning the number of the standard tableaux on "cylindric" skew diagrams. Our formula can be seen as an extension of Naruse's hook formula for skew diagrams. Moreover, we prove our conjecture in some special cases.
Published Date 2022-01
Publication Title Mathematical Journal of Okayama University
Volume volume64
Issue issue1
Publisher Department of Mathematics, Faculty of Science, Okayama University
Start Page 191
End Page 213
ISSN 0030-1566
NCID AA00723502
Content Type Journal Article
language 英語
Copyright Holders Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
FullText URL mjou_064_117_141.pdf
Author Wang, Qi|
Abstract As the first attempt to classify τ-tilting finite two-point algebras, we have determined the τ-tilting finiteness for minimal wild two-point algebras and some tame two-point algebras.
Keywords Support τ-tilting modules τ-tilting finite two-point algebras
Published Date 2022-01
Publication Title Mathematical Journal of Okayama University
Volume volume64
Issue issue1
Publisher Department of Mathematics, Faculty of Science, Okayama University
Start Page 117
End Page 141
ISSN 0030-1566
NCID AA00723502
Content Type Journal Article
language 英語
Copyright Holders Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
FullText URL mjou_064_143_151.pdf
Author Aokage, Kazuya | Tabata, Sumitaka | Yamada, Hiro-Fumi|
Abstract A quantum version of classical Sylvester-Franke theorem is presented. After reviewing some representation theory of the quantum group GL<sub>q</sub> (n, C), the commutation relations of the matrix elements are verified. Once quantum determinant of the representation matrix is defined, the theorem follows naturally
Keywords Quantum general linear group Sylvester-Franke theorem
Published Date 2022-01
Publication Title Mathematical Journal of Okayama University
Volume volume64
Issue issue1
Publisher Department of Mathematics, Faculty of Science, Okayama University
Start Page 143
End Page 151
ISSN 0030-1566
NCID AA00723502
Content Type Journal Article
language 英語
Copyright Holders Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
FullText URL mjou_064_047_061.pdf
Author Yamanaka, Satoshi|
Abstract The notion of weakly separable extensions was introduced by N. Hamaguchi and A. Nakajima as a generalization of separable extensions. The purpose of this article is to give a characterization of weakly separable polynomials in skew polynomial rings. Moreover, we shall show the relation between separability and weak separability in skew polynomial rings of derivation type.
Keywords separable extension weakly separable extension skew polynomial ring derivation
Published Date 2022-01
Publication Title Mathematical Journal of Okayama University
Volume volume64
Issue issue1
Publisher Department of Mathematics, Faculty of Science, Okayama University
Start Page 47
End Page 61
ISSN 0030-1566
NCID AA00723502
Content Type Journal Article
language 英語
Copyright Holders Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
FullText URL mjou_064_013_029.pdf
Author Seita, Kohei|
Abstract Let G be a finite group. In 1970s, T. Petrie defined the Smith equivalence of real G-modules. The Smith set of G is the subset of the real representation ring consisting of elements obtained as differences of Smith equivalent real G-modules. Various results of the topic have been obtained. The d-Smith set of G is the set of all elements [V ]−[W] in the Smith set of G such that the H-fixed point sets of V and W have the same dimension for all subgroups H of G. The results of the Smith sets of the alternating groups and the symmetric groups are obtained by E. Laitinen, K. Pawa lowski and R. Solomon. In this paper, we give the calculation results of the d-Smith sets of the alternating groups and the symmetric groups. In addition, we give the calculation results of the d-Smith sets of Cartesian products of the alternating groups and finite elementary abelian 2-groups.
Keywords Real G-module Smith equivalence Oliver group alternating group
Published Date 2022-01
Publication Title Mathematical Journal of Okayama University
Volume volume64
Issue issue1
Publisher Department of Mathematics, Faculty of Science, Okayama University
Start Page 13
End Page 29
ISSN 0030-1566
NCID AA00723502
Content Type Journal Article
language 英語
Copyright Holders Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
FullText URL mjou_064_109_116.pdf
Author Yagita, Nobuaki|
Abstract Let p be a prime number. For a given finite group G, let gr<sup>*</sup><sub>&gamma;</sub>(BG) be the associated ring of the gamma filtration of the topological K-theory for the classifying space BG. In this paper, we study gr<sup>*</sup><sub>&gamma;</sub>(BG) when G are abelian p-groups which are not elementary. In particular, we extend related Chetard’s results for such 2-groups to p-groups for odd p.
Keywords K-theory gamma fitration abelian p-group
Published Date 2022-01
Publication Title Mathematical Journal of Okayama University
Volume volume64
Issue issue1
Publisher Department of Mathematics, Faculty of Science, Okayama University
Start Page 109
End Page 116
ISSN 0030-1566
NCID AA00723502
Content Type Journal Article
language 英語
Copyright Holders Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
FullText URL mjou_064_153_186.pdf
Author Nishiyama, Yuta|
Abstract In this article, we introduce some identities obtained from the inner products of some symmetric polynomials including the Macdonald polynomials. These identities are obtained not only from the inner products, but also by constructing certain bijections. The bijections are constructed through transforming the Young diagrams of partitions.
Keywords Macdonald polynomials Young diagram bijective proof
Published Date 2022-01
Publication Title Mathematical Journal of Okayama University
Volume volume64
Issue issue1
Publisher Department of Mathematics, Faculty of Science, Okayama University
Start Page 153
End Page 186
ISSN 0030-1566
NCID AA00723502
Content Type Journal Article
language 英語
Copyright Holders Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
FullText URL mjou_064_187_190.pdf
Author Puthenpurakal, Tony J. |
Abstract Let K be a field and consider the standard grading on A = K[X<sub>1</sub>, ... ,X<sub>d</sub>]. Let I, J be monomial ideals in A. Let I<sub>n</sub>(J) = (I<sup>n</sup> : J<sup>&infin;</sup>) be the n<sup>th</sup> symbolic power of I with respect to J. It is easy to see that the function f<sup>I</sup> <sub>J</sub> (n) = e<sub>0</sub>(I<sub>n</sub>(J)/I<sup>n</sup>) is of quasi-polynomial type, say of period g and degree c. For n ≫ 0 say<br> <br> f<sup>I</sup><sub>J</sub> (n) = a<sub>c</sub>(n)n<sup>c</sup> + a<sub>c−1</sub>(n)n<sup>c−1</sup> + lower terms,<br> <br> where for i = 0, ... , c, a<sub>i</sub> : N → Q are periodic functions of period g and a<sub>c</sub> &ne;0. In [4, 2.4] we (together with Herzog and Verma) proved that dim I<sub>n</sub>(J)/I<sup>n</sup> is constant for n ≫ 0 and a<sub>c</sub>(−) is a constant. In this paper we prove that if I is generated by some elements of the same degree and height I ≥ 2 then a<sub>c−1</sub>(−) is also a constant.
Keywords quasi-polynomials monomial ideals symbolic powers
Published Date 2022-01
Publication Title Mathematical Journal of Okayama University
Volume volume64
Issue issue1
Publisher Department of Mathematics, Faculty of Science, Okayama University
Start Page 187
End Page 190
ISSN 0030-1566
NCID AA00723502
Content Type Journal Article
language 英語
Copyright Holders Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
FullText URL mjou_064_215_225.pdf
Author Hyodo, Fumitake|
Abstract This paper focuses on the theory of the Hecke rings associated with the general linear groups originally studied by Hecke and Shimura et al., and moreover generalizes its notions to Hecke rings associated with the automorphism groups of certain algebras. Then, in the case of the Heisenberg Lie algebra, we show an analog of the classical theory.
Keywords Hecke rings noncommutative rings
Published Date 2022-01
Publication Title Mathematical Journal of Okayama University
Volume volume64
Issue issue1
Publisher Department of Mathematics, Faculty of Science, Okayama University
Start Page 215
End Page 225
ISSN 0030-1566
NCID AA00723502
Content Type Journal Article
language 英語
Copyright Holders Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
FullText URL mjou_063_061_086.pdf
Author Itaba, Ayako| Matsuno, Masaki|
Abstract Classification of AS-regular algebras is one of the main interests in non-commutative algebraic geometry. Recently, a complete list of superpotentials (defining relations) of all 3-dimensional AS-regular algebras which are Calabi-Yau was given by Mori-Smith (the quadratic case) and Mori-Ueyama (the cubic case), however, no complete list of defining relations of all 3-dimensional AS-regular algebras has not appeared in the literature. In this paper, we give all possible defining relations of 3-dimensional quadratic AS-regular algebras. Moreover, we classify them up to isomorphism and up to graded Morita equivalence in terms of their defining relations in the case that their point schemes are not elliptic curves. In the case that their point schemes are elliptic curves, we give conditions for isomorphism and graded Morita equivalence in terms of geometric data.
Keywords AS-regular algebras geometric algebras quadratic algebras nodal cubic curves elliptic curves Hesse form Sklyanin algebras
Published Date 2021-01
Publication Title Mathematical Journal of Okayama University
Volume volume63
Issue issue1
Publisher Department of Mathematics, Faculty of Science, Okayama University
Start Page 61
End Page 86
ISSN 0030-1566
NCID AA00723502
Content Type Journal Article
language 英語
Copyright Holders Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University
FullText URL mjou_063_167_173.pdf
Author Puthenpurakal, Tony J.|
Abstract Let (A, m) be an excellent normal domain of dimension two. We define an m-primary ideal I to be a pg -ideal if the Rees algebra A[It] is a Cohen-Macaulay normal domain. If A has infinite residue field then it follows from a result of Rees that the product of two pg ideals is pg . When A contains an algebraically closed field k ∼= A/m then Okuma, Watanabe and Yoshida proved that A has pg -ideals and furthermore product of two pg -ideals is a pg ideal. In this article we show that if A is an excellent normal domain of dimension two containing a field k ∼= A/m of characteristic zero then also A has pg -ideals.
Keywords pg -ideal normal Rees rings Cohen-Macaulay rings stable ideals
Published Date 2021-01
Publication Title Mathematical Journal of Okayama University
Volume volume63
Issue issue1
Publisher Department of Mathematics, Faculty of Science, Okayama University
Start Page 167
End Page 173
ISSN 0030-1566
NCID AA00723502
Content Type Journal Article
language 英語
Copyright Holders Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University
FullText URL mjou_063_087_105.pdf
Author Zdzisław, Wojtkowiak|
Abstract The fact that the double zeta values ζ(n, m) can be written in terms of zeta values, whenever n+m is odd is attributed to Euler. We shall show the weak version of this result for the l-adic Galois realization.
Keywords multiple zeta values Galois groups fundamental groups
Published Date 2021-01
Publication Title Mathematical Journal of Okayama University
Volume volume63
Issue issue1
Publisher Department of Mathematics, Faculty of Science, Okayama University
Start Page 87
End Page 105
ISSN 0030-1566
NCID AA00723502
Content Type Journal Article
language 英語
Copyright Holders Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University
FullText URL mjou_063_001_014.pdf
Author Graef, John R.| Beldjerd, Djamila| Remili, Moussadek|
Abstract In this paper, sufficient conditions are established for the stability, boundedness and square integrability of solutions for some non-linear neutral delay differential equations of third order. Lyapunov’s direct method is used to obtain the results.
Keywords boundedness stability square integrability
Published Date 2021-01
Publication Title Mathematical Journal of Okayama University
Volume volume63
Issue issue1
Publisher Department of Mathematics, Faculty of Science, Okayama University
Start Page 1
End Page 14
ISSN 0030-1566
NCID AA00723502
Content Type Journal Article
language 英語
Copyright Holders Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University
FullText URL mjou_063_107_122.pdf
Author Kato, Ryo| Shimomura, katsumi|
Abstract In recent years, Liu and his collaborators found many non-trivial products of generators in the homotopy groups of the sphere spectrum. In this paper, we show a result which not only implies most of their results, but also extends a result of theirs.
Keywords Stable homotopy of spheres Adams spectral sequence May spectral sequence
Published Date 2021-01
Publication Title Mathematical Journal of Okayama University
Volume volume63
Issue issue1
Publisher Department of Mathematics, Faculty of Science, Okayama University
Start Page 107
End Page 122
ISSN 0030-1566
NCID AA00723502
Content Type Journal Article
language 英語
Copyright Holders Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University
FullText URL mjou_063_133_151.pdf
Author Aokage, Kazuya|
Abstract We derive the Schur function identities coming from the tensor products of the spin representations of the symmetric group Sn. We deal with the tensor products of the basic spin representation V (n) and any spin representation V λ (λ ∈ SP (n)). The characteristic map of the tensor product ζn ⊗ ζλ is described by Stembridge[4] for the case of odd n. We consider the case n is even.
Keywords symmetric group symmetric function projective representation
Published Date 2021-01
Publication Title Mathematical Journal of Okayama University
Volume volume63
Issue issue1
Publisher Department of Mathematics, Faculty of Science, Okayama University
Start Page 133
End Page 151
ISSN 0030-1566
NCID AA00723502
Content Type Journal Article
language 英語
Copyright Holders Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University
FullText URL mjou_063_123_131.pdf
Author Lee, Min Ho|
Abstract Given Jacobi forms, we determine associated Jacobi-like forms, whose coefficients are quasimodular forms. We then use these quasimodular forms to construct differential operators on modular forms, which are expressed in terms of the Fourier coefficients of the given Jacobi forms.
Keywords Jacobi forms Jacobi-like forms modular forms quasimodular forms
Published Date 2021-01
Publication Title Mathematical Journal of Okayama University
Volume volume63
Issue issue1
Publisher Department of Mathematics, Faculty of Science, Okayama University
Start Page 123
End Page 131
ISSN 0030-1566
NCID AA00723502
Content Type Journal Article
language 英語
Copyright Holders Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University