Automorphic forms of several variables and spherical functions of homoge-neous spaces

多变量的自守形式与齐次空间的球函数

• 批准号: 09440016
• 负责人: YAMAZAKI Tadashi
• 金额: $ 5.5万
• 依托单位: KOBE UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09440016/
• 关键词: automorphic form; Hecke algebra; spherical function

The spherical function or the Shintani function of homogeneous spaces are important in order to study the Fourier expansion of period of automorphic forms and L-functions associated to automorphic forms.We studied mainly the Shintani function of the classical groups. in particular we proved uniqueness and existence of the Shintani function and in some cases we obtained explicit formulas for them. We applied them to examine analytic and arithmetic properties of automorphic L-functions. (Muarase-Sugano)It would be our next objective to define suitable geometrical objects associated to spherical subgroups and to interpret the Shintani function in terms of their cohomology groups.

齐性空间的球函数或Shintani函数对于研究自守形式的周期的Fourier展开以及与自守形式相关的L-函数是很重要的，本文主要研究了经典群的Shintani函数。特别地，我们证明了Shintani函数的存在性和唯一性，并在某些情况下得到了它们的显式公式。我们应用它们来研究自守L-函数的分析和算术性质。（Muarase Sugano）这将是我们的下一个目标，定义适当的几何对象相关联的球面子群和解释的Shintani函数在其上同调群。

项目成果

M.Saito: "Hypergeometric polynomials and Integer Programming" Compositio Math.(印刷中). (1999)

M.Saito：“超几何多项式和整数规划”复合数学（印刷中）。

M.Saito: "Signature defects and eta functions of degenerations of abelian varieties" Japan.J.Math.23-2. 319-364 (1997)

M.Saito：“阿贝尔簇退化的特征缺陷和 eta 函数”Japan.J.Math.23-2。

M.Saito: "Hypergeometric polynomials and Integer Pro-gramming" Compositio Math.(in press). (1999)

M.Saito：“超几何多项式和整数规划”复合数学（正在出版）。

K.Watanabe: "Cousin problems and holomorphic cocycles" Math.Japonica. 48-2. 217-221 (1998)

K.Watanabe：“表弟问题和全纯余循环”Math.Japonica。

N.Takayama: "Compactifications of the configuration space of 6 points of the projective plane and fundamental solutions of the hypergeometric system of type (3, 6)" Tohoku Mathematical Journal. 49. 379-413 (1997)

N.Takayama：“射影平面 6 点配置空间的紧化和 (3, 6) 型超几何系统的基本解”东北数学杂志。