1996 Fiscal Year Final Research Report Summary
Research on automorphic representations
| Project/Area Number |
06402001
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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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 | KYOTO UNIVERSITY |
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Principal Investigator |
YOSHIDA Hiroyuki Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (40108973)
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| Co-Investigator(Kenkyū-buntansha) |
UMEDA Toru Kyoto Univ., Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (00176728)
HIRAI Takeshi Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (70025310)
HIRAGA Kaoru Kyoto Univ., Graduate School of Science, Instructor, 大学院・理学研究科, 助手 (10260605)
IKEDA Tamotsu Kyoto Univ., Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (20211716)
HIJIKATA Hiroaki Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (00025298)
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| Project Period (FY) |
1994 – 1996
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| Keywords | L-function / Lie group / period of an abelian variety |
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| Research Abstract |
H.Yoshida studied periods of Hilbert modular forms and proved Shimura's conjectures on P,Q-invariants. He also studied the derivatives of Artin's L-functions at s=0 and found a relation with periods of abelian varieties with complex multiplication. This relation can be sharpened by the notion of "absolute CM-periods".
T.Ikeda studied residues of Eisenstein series and proved a Siegel-Weil type formula when Eisenstein series does not converge.
K.Hiraga studied the multiplicity of a discrete series representation with which it occurs in L^2 (GAMMA/G), where G is a semisimple Lie group and GAMMA is a discrete subgroup.
T.Umeda studied the notion of dual reductive pair in the case of quatum groups ; he generalized Capelli type identities for this case.
H.Hijikata conjectured an approximation theorem for semisimple algebras over the quotient field of a Dedekind domain ; related with this conjecture, he obtained many results on orders and lattices.
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