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

在这个项目的两年里，我们每月分别在东京大学的驹场校区和科比大学举办研讨会。这两次研讨会是交流的中心，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“小”的李群上的显式调和分析，我们取得了比项目之前想象的更大的进展。通过这些结果，我们现在有了新的问题，例如，构建像庞加莱系列这样的全局对象或研究这些对象的基本属性。（TSUUKI，Masao，PDF of JSPS ;宫崎，Takuya，PDF of JSPS ; HAYATA，Takahiro，Graduate Student of科比大学），研究了各种广义球函数（即. e.标准表示的矩阵系数、惠特克函数等）等级1或等级2的。几 ...更多信息 Arakawa将关于多元全纯模方程的经典和基本结果推广到Jacobi群上。与Miyage Edu的TAKASE一起。大学，小田和荒川每月组织一次关于“自守形式”的研讨会，使其成为该项目的中心。这次研讨会的目的之一是获得有关Selebrg迹公式的一些基本知识。一些年轻的观众开始熟悉这个主题的标准事实。菅野和村濑一直在发展他们的理论自守L-函数的经典群体使用新丹函数。他们发表了GL_n的情况，酉群的情况也将很快作为讲义出现。Ibukiyama继续共同工作齐藤弘对塞尔贝格跟踪公式。他还开始了一项联合工作与胜田Hongori室兰大学的傅立叶系数爱森斯坦系列。山崎和村濑每月在科比大学组织一次研讨会。少

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