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L-function of automorphic forms of many variables, Selberg trace fromula, and related harmonic analysis.

多变量自守形式的 L 函数、Selberg 迹公式以及相关调和分析。

基本信息

批准号：
07304001
负责人：
ODA Takayuki
金额：
$ 1.73万
依托单位：
the University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1995
资助国家：
日本
起止时间：
1995 至 1996
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07304001/
关键词：
L-function automorphic forms spherical functions harmonic analysis 跡公式

项目摘要

For two years of the project, we had monthly seminars at Komaba Compus of Tokyo University and at Kobe University, respectively. These two seminars had been the centers of the communications.On the mathematical contents, we cannot yet attain the main purpose for the investigation of the Selberg trace formula. However on the other themes, for example, on the explicit harmonic analysis on the relatively "small" Lie groups, we had more progress than imagined first before the project By these results, we have now new problems, say, the construction of global objects like Poincare' series or the investigation of the fundamental properties of these objects.The head of the project Oda, collaborated with young people (TSUZUKI,Masao, PDF of JSPS ; MIYAZAKI,Takuya, PDF of JSPS ; HAYATA,Takahiro, Graduate Student of Kobe Univ), investigated various kind of generalized spherical functions (i. e. matrix coefficients of standard representations, Whittaker functions, ect.) of rank 1 or rank 2. A few … More joint papers on this theme are submitted to some journals.Arakawa extended various important classical and fundamental results on holomorphic modular foums of many variables to the Jacobi groups. Together with TAKASE of Miyage Edu. Univ., Oda and Arakawa organized a monthly seminar on "Automorphic Forms", to make it as a center of the project.Among the purposes of this seminar, one is to obtain some fundamental knowledge on Selebrg trace formulae. Some of young audience become familier with standard facts on this theme.Sugano and Murase have been developping their theory of automorphic L-functions on classical groups using Shintan functions. They pubslished the case of GL_-n and the case of unitary groups will also appear soon as a lecture note. Ibukiyama continued the joint work SAITO Hiroshi on Selberg trace formula. He started also a joint work with KATSURADA Hidenori of Muroran University on Fourier coefficients on Eisenstein series. Yamazaki and Murase orgenized a monthly seminar at Kobe University. Less

在这个项目的两年时间里，我们每月分别在东京大学和神户大学的小叶校区举办研讨会。这两个研讨会一直是交流的中心，在数学内容上，我们还不能达到研究塞尔伯格迹公式的主要目的。然而，在其他主题上，例如在相对较小的李群的显式调和分析方面，这些结果取得了比项目开始之前想象的更多的进展，现在我们有了新的问题，比如像Poincare级数这样的全局对象的构造或这些对象的基本性质的研究。Oda项目的负责人与年轻人(JSPS的Tsuzuki，Masao，PDF；JSPS的Miyazaki，Takuya，PDF；神户大学研究生Hayata，Takahiro，PDF；神户大学研究生Hayata，Takahiro)合作，研究了各种广义球函数(即标准表示的矩阵系数，Whittaker函数等)。排名1或排名2的。几个…关于这一主题的更多联合论文被提交到一些期刊上。荒川将关于多元全纯模公式的各种重要的经典和基本结果推广到Jacobi群。和宫崎骏的Takase一起。大学、小田和荒川组织了每月一次的“自同构形”研讨会，使之成为该项目的中心。这次研讨会的目的之一是获得一些关于塞勒布勒迹公式的基本知识。一些年轻的听众对这一主题的标准事实变得更加熟悉。Sugano和Murase一直在利用Shintan函数在经典群上发展他们的自同构L函数理论。他们公布了GL_n的情况，酉群的情况也将很快作为课堂讲稿出现。Ibukiyama继续与齐藤博共同研究塞尔伯格示踪公式。他还开始与穆罗兰大学的KATSURADA Hidnowi共同研究Eisenstein级数的傅立叶系数。山崎和村上春树在神户大学组织了一个每月一次的研讨会。较少