| Co-Investigator(Kenkyū-buntansha) |
YAMAZAKI Tadashi Kobe Univ., Fac. of Science, Professor, 理学部, 教授 (30011696)
MURASE Atsushi Kyoto Sangyo University, Fac. of Science, Professor, 理学部, 教授 (40157772)
SUGANO Takashi Hiroshima Univ., Fac. of Science, Associate Professor, 理学部, 助教授 (30183841)
IBUKIYAMA Tomoyoshi Osaka Univ., Graduate School of Science, Professor, 理学研究科, 教授 (60011722)
ARAKAWA Tsuneo St. Paulo University, Fac. of Science, Dep't of Math., Professor, 理学部, 教授 (60097219)
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| Research Abstract |
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
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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
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