Explicit study on automorphic structure in algebra and zeta functions.

代数和 zeta 函数中自守结构的显式研究。

• 批准号: 13304002
• 负责人: IBUKIYAMA Tomoyoshi
• 金额: $ 25.71万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13304002/
• 关键词: zeta function; modular form; number theory; quadratic form; vertex operator algebra; L-function; prehomogeneous vector space; algebraic combinatorics; ゼータ関数; 微分作用素; 志村対応; エータ関数; 微分方程式; コード理論; 共形場の理論; テータ関数; モジュラー多様体

In these four years, the principal researcher of this subject organized a conference at Oberwol-fach, three Spring Confecences, two Autumn Workshops (one of which is Japan-Germany Seminar supported by JSPS), Mini-workshop on Number Theory, and Meeting on Modular Forms and Zeta Functions, hence 8 conferences in total, and studied effectively with many foreign researchers and cooperative researchers in Japan, In particular, in Spring Conference, we focused to communicate with wide areas arround modular forms, and took Graded rings of modular forms, Vertex operator algebras in first and second one, and more mixed areas in the third one. We published five Proceedings of 970 total pages. More concretely, the principal researcher proposed a conjecture on Shimura type correspondence between Siegel modular forms of integral and half integral weight, studied structures of scalar valued and vector valued Siegel modular forms and differential operators, Borcherds product expression, holonomic system coming from differential operators on modular forms, positivity of eta products, Koecher-Maass series of forms obtained by lifting, modular forms of rational weight. As it can be seen from the list of their papers, the other researchers of our project also actively studied on conformal field theory, spherical and Whittaker functions, prehomogenous vector spaces, modular forms on unitary groups, elliptic root systems, p-adic modular forms, L-packet, adele geometry, converse theorem, vertex operator algebras, combinatorial designs, weakly spherical spaces, inverse Galois problem and CAP forms.

在这四年中，该主题的首席研究人员在Oberwol-Fach举办了一次会议，三个春季邦联，两个秋季研讨会（其中一个是JSP支持的日本 - 喜剧研讨会），关于数字理论的小型工作坊，以及关于模块化形式和ZETA功能的小型工作室，因此在许多人中进行了8个会议，因此与许多人进行了启动，并在许多春季进行了专业的会议，并在许多方面进行了专业研究，并提供了春季研究，并提供了春季的参与者，并提供了春季研究，并提供了春季的参与者，并提供了春季的参与者，并与之相关。与广阔的区域沟通模块化形式，并在第一个和第二个中取出了模块化形式的分级环，顶点操作员代数，以及第三个区域中更多的混合区域。我们发布了970个总页面的五个程序。 More concretely, the principal researcher proposed a conjecture on Shimura type correspondence between Siegel modular forms of integral and half integral weight, studied structures of scalar valued and vector valued Siegel modular forms and differential operators, Borcherds product expression, holonomic system coming from differential operators on modular forms, positivity of eta products, Koecher-Maass series of forms obtained by lifting, modular理性体重的形式。 As it can be seen from the list of their papers, the other researchers of our project also actively studied on conformal field theory, spherical and Whittaker functions, prehomogenous vector spaces, modular forms on unitary groups, elliptic root systems, p-adic modular forms, L-packet, adele geometry, converse theorem, vertex operator algebras, combinatorial designs, weakly spherical spaces, inverse加洛伊斯问题和上限形式。

项目成果

Convergence of the zeta functions of prehomogeneous vector spaces

预齐次向量空间 zeta 函数的收敛性

• 发表时间: 2003
• 期刊: Nagoya Math.J. 170
• 作者: K.Nishiyama;Zhu;Chen-bo;西山 享;T.Matsuki;H.Saito
• 通讯作者: H.Saito

Polyhedra dual to the Weyl Chamber decomposition : A precis

韦尔室分解的对偶多面体：概要

• 发表时间: 2004
• 期刊: Publ. RIMS, Kyoto Univ 40
• 作者: K.;Saito
• 通讯作者: Saito

Quasi-modular forms and trace functions associated to free boson and lattice vertex operator algebras

• DOI: 10.1155/s1073792801000204
• 发表时间: 2001-01-01
• 期刊: INTERNATIONAL MATHEMATICS RESEARCH NOTICES
• 影响因子: 1
• 作者: Dong, CY;Mason, G;Nagatomo, K
• 通讯作者: Nagatomo, K

On Some Gelfand Pairs and Commutative Association Schemes

一些格尔芬德对和交换关联方案

• 发表时间: 2002
• 期刊: Proceedings of Meeting on combinatorial number theory and algebraic combinatorics(Yamagata Univ.)
• 作者: E.Bannai;H.Tanaka
• 通讯作者: H.Tanaka

Primitive automorphic forms (in Japanese)

原始自守形式（日​​语）

• 发表时间: 2002
• 期刊: Top frontier of mathematics and challenge to 21 century, (translation from "Mathematics Unlimited 2001")(Springer Verlag Tokyo)
• 作者: E.Bannai;H.Tanaka;K.Saito
• 通讯作者: K.Saito