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Arithmetic of automorphic forms of many variable : reconstruction of the foundation

多变量自守形式的算术：基础的重建

基本信息

批准号：
09440007
负责人：
ODA Takayuki
金额：
$ 6.98万
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：
1997
资助国家：
日本
起止时间：
1997 至 1999
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09440007/
关键词：
Automorphic forms L-functions Spherical functions Modular forms Special functions L関数 L-関数

项目摘要

As planned in our application, at Tokyo and at Kobe we had a series of monthly seminars. Since we have already reported about them in the annual reports, here we do not write about them. We also omit the details about the workshops at RIMS, Kyoto University and the summer schools. The proceedings on these meetings are available. The head investigator Oda in a joint work with Takahiro HAYATA (Yamagata Univ.) and Harutaka KOSEKI (Mie University) obtained an explicit formula for matrix coefficients of the middle discrete series of SU(2,2). Added to this he also obtained explicit formulae of matrix coefficients for the large discrete series of SU(2,2) and Sp(2,R). Moreover in a joint paper with Masao TSUZUKI (Sophia Univ.) he constructed Green functions of modular divisors on arithmetic quotients of certain bounded symmetric domains, as automorphic forms. We also explain the outline of the fruits of the research by the investigators joined to this plan. This result has not only have applic … More ations for the dimension of spaces of automorphic forms, but also theoretically significance. Ibukiyama and Saito had remarkable results on the evaluation of the special values of the zeta functions of prehomogeneous vector spaces. This result has not only application to the explicit dimension formulae of the spaces of automorphic forms, but also theoretically very important meaning. The investigation of p-adic spherical functions by Sato and Hironaka made much progress. The new point among others is that they can handle also the case of "ramified" spherical functions. The joint work of Murase and Sugano also advanced. Their work of the primitive theta function of SU(2,1) is one interesting result. But also the is a progress in the theory of automorphic L-functions on orthogonal groups A joint work with Shin-ichi Kato (Kyoto Univ.) on p-adic spherical functions is one of fruits. Watanabe together with Masanori Morishita (Kanazawa Univ.) pushed forward the investigation of Hermite constants for algebraic groups, Which is so to speak a non-abelian version of "Geometry of Numbers". The result of Katsurada is also interesting by regarding it as an investigation of ramified p-adic spherical functions. Less

按照我们申请时的计划，我们在东京和科比举办了一系列每月一次的研讨会。由于我们已经在年度报告中报告了这些问题，因此在此不再赘述。我们也省略了RIMS，京都大学和暑期学校的工作坊的细节。可查阅这些会议的记录。首席研究员小田在与早田孝弘（山形大学）的联合工作。Harutaka KOSEKI（三重大学）得到了SU（2，2）中间离散级数矩阵系数的一个显式公式。此外，他还获得了明确的公式矩阵系数的大型离散系列SU（2，2）和Sp（2，R）。此外，在与Masao TSUUKI（Sophia Univ.）他构建了绿色功能的模块化因子的算术代数的某些有界对称域，作为自守形式。我们还解释了加入该计划的调查人员的研究成果的概要。这一结果不仅具有实际应用价值， ...更多信息自守形式空间的维数的一些性质，也具有理论意义。Ibukiyama和Saito对预齐次向量空间的zeta函数的特殊值的评价有着显著的成果。这一结果不仅对自守型空间的显式维数公式有应用，而且在理论上也有很重要的意义。Sato和Hironaka对p-adic球函数的研究取得了很大进展。新的一点是，他们也可以处理的情况下，“分歧”球函数。村濑和菅野的联合工作也取得了进展。他们对SU（2，1）的原始theta函数的研究是一个有趣的结果。同时也是正交群上自守L-函数理论的一个进展。p-adic球面函数的研究是这方面的成果之一。渡边与Masanori Morishita（金泽大学）推进了代数群Hermite常数的研究，可以说是“数的几何”的非交换版本。Katsurada的结果也是有趣的，因为它被视为一个调查的分歧p-adic球函数。少