1988 Fiscal Year Final Research Report Summary
Research on automorphic forms
| Project/Area Number |
62540039
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
代数学・幾何学
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| Research Institution | Kyoto University |
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Principal Investigator |
YOSHIDA Hiroyuki Department of mathematics, Faculty of Science, Kyoto Univ. Associate Professor, 理学部, 助教授 (40108973)
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| Co-Investigator(Kenkyū-buntansha) |
MARUYAMA Masaki Associate Professor, Dept. of Math. Fac. of Sci Kyoto Univ., 理学部, 助教授 (50025459)
UENO Kenji Professor, Dept. of Math. Fac. of Sci Kyoto Univ., 理学部, 教授 (40011655)
UEDA Masaru Instructor, Dept. of Math. Fac. of Sci Kyoto Univ., 理学部, 助手 (80193811)
ISHII Hidenori Instructor, Dept., of Math. Fac. of Sci., Kyoto Univ., 理学部, 助手 (60159671)
HIJIKATA Hiroaki Professor, Dept. of Math., Fac. of Sci. Kyoto Univ, 理学部, 教授 (00025298)
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| Project Period (FY) |
1987 – 1988
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| Keywords | Automorphic form / L-function / Unitarizability / ユニタリー表現 |
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| Research Abstract |
H. Yoshida has investigated representations of finite groups on Siegel modular forms in terms of theta series and generalized Hecke's theory. He has calculated zeros of various L-functions associated with automorphic forms. He also determined unitarizable principal series representations completely for p-adic Chevalley groups of classical type.
H. Hijikata has proved that the restriction to an anisotropic torus of an arbitrary smooth irreducible representation of GL(2) over a p-adic field is multiplicity free. He (with A.Pizer, T. Schemanske) has obtained a definitive result on the classical basis problem on theta series.
M.Ueda has obtained interesting results on modular forms of half integral weight, using twisting poerators. His results suggest the existence of the theory of new forms also for the half integral weight case.
H. Ishii proved a criterion for the non-existence of an abelian variety with everywhere good reduction.
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