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

在两年的项目中，我们每月分别在东京大学的小叶校区和神户大学举办研讨会。这两个讨论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“小”李群的显式调和分析上，我们取得了比项目开始前想象的更多的进展。通过这些结果，我们现在有了新的问题，比如，像庞加莱级数这样的全局对象的构建，或者对这些对象的基本性质的研究。该项目的负责人Oda与年轻人（TSUZUKI,Masao, JSPS PDF； MIYAZAKI,Takuya, JSPS PDF； HAYATA,Takahiro，神户大学研究生）合作，研究了1级或2级的各种广义球函数（即标准表示的矩阵系数，Whittaker函数等）。更多关于这个主题的联合论文被提交给一些期刊。Arakawa将许多关于多变量全纯模形式的重要经典和基本结果推广到Jacobi群。与Miyage Edu的TAKASE一起。大学、Oda和Arakawa组织了一个关于“自同构形式”的月度研讨会，使其成为项目的中心。这次研讨会的目的之一是获得关于Selebrg轨迹公式的一些基本知识。一些年轻的观众熟悉了这个主题的标准事实。Sugano和Murase利用Shintan函数发展了经典群上的自同构l函数理论。他们发表了gl_n的例子，幺正群的例子也将很快出现在课堂讲稿中。秋山继续着斋藤宏对塞尔伯格追查公式的联合工作。他还与Muroran大学的KATSURADA Hidenori开始了关于爱森斯坦级数的傅里叶系数的合作研究。山崎和村濑在神户大学组织了每月一次的研讨会。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