| Project/Area Number |
09440007
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | The University of Tokyo |
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Principal Investigator |
ODA Takayuki Professor, the Graduate School of Math. Sci., the Uni. of Tokyo, 大学院・数理科学研究科, 教授 (10109415)
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| Co-Investigator(Kenkyū-buntansha) |
SAITO Hiroshi Prof. Grad. School of Hum. & Env. Studies, Kyoto Univ., 大学院・人間環境学研究科, 教授 (20025464)
IBUKIYAMA Tomoyoshi Prof. Grad. Sch. of Sci., Osaka Univ., 大学院・理学研究科, 教授 (60011722)
ARAKAWA Tsuno Prof. Faculty of Science, St. Paul Univ., 理学部, 教授 (60097219)
HIRONAKA Yumiko Prof. Fac. of Edu., Waseda Univ., 教育学部, 教授 (10153652)
TAKASE Kouichi ASS. Prof. Fac. of Edu., Miyagi Edu. Univ., 教育学部, 助教授 (60197093)
山崎 正 神戸大学, 理学部, 教授 (30011696)
菅野 孝史 金沢大学, 理学部, 教授 (30183841)
村瀬 篤 京都産業大学, 理学部, 教授 (40157772)
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| Project Period (FY) |
1997 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥10,900,000 (Direct Cost: ¥10,900,000)
Fiscal Year 1999: ¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 1998: ¥4,400,000 (Direct Cost: ¥4,400,000)
Fiscal Year 1997: ¥3,600,000 (Direct Cost: ¥3,600,000)
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| Keywords | Automorphic forms / L-functions / Spherical functions / Modular forms / Special functions / L関数 / L-関数 |
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| Research Abstract |
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
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