1999 Fiscal Year Final Research Report Summary
Research on nearly holomorphic modular forms
| Project/Area Number |
10640010
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Tokyo Institute of Technology |
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Principal Investigator |
MIZUMOTO Shin-ichiro TOKYO INSTITUTE OF TECHNOLOGY, Graduate School of Science and Engineering, Associate Prof., 大学院・理工学研究科, 助教授 (90166033)
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| Co-Investigator(Kenkyū-buntansha) |
TSUJI Hajime TOKYO INSTITUTE OF TECHNOLOGY, Graduate School of Science and Engineering, Associate Prof., 大学院・理工学研究科, 助教授 (30172000)
SHIGA Hiroshige TOKYO INSTITUTE OF TECHNOLOGY, Graduate School of Science and Engineering, Professor, 大学院・理工学研究科, 教授 (10154189)
KUROKAWA Nobushige TOKYO INSTITUTE OF TECHNOLOGY, Graduate School of Science and Engineering, Professor, 大学院・理工学研究科, 教授 (70114866)
NAKAYAMA Chikara TOKYO INSTITUTE OF TECHNOLOGY, Graduate School of Science and Engineering, Research Associate, 大学院・理工学研究科, 助手 (70272664)
HATTORI Toshiaki TOKYO INSTITUTE OF TECHNOLOGY, Graduate School of Science and Engineering, Associate Prof., 大学院・理工学研究科, 助教授 (30251599)
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| Project Period (FY) |
1998 – 1999
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| Keywords | Atomorphic forms / L-functions / Discrete groups |
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| Research Abstract |
Mizumoto studied the central zeros of the Rankin L-functions associated to a pair of holomorphic modular forms for SL(2, Z); he obtained a nonvanishing result for them.
Kurokawa studied the spectra of Laplace operators on categories. He proved its semipositivity and obtained some asymptotic results. The results are expected to have some connection with zeta functions of categories.
Shiga proved analogy between the limit set of Kleininan groups and the Julia set (as a function-theoretic set) in complex dynamical systems. He also studied rigidity and finiteness of holomophic mappings on complex hyperbolic manifolds.
Tsuji studied applications of singular hermitian metrics. In particular, he obtained a satisfactory result on the structure of canonical rings and on the quasi-projectivity of moduli spaces of polarized algebraic varieties.
Hattori studied quasi-isometry invariants of discrete groups. In particular, he investigated uniform lattices in Lie groups.
Nakayama studied log geometry for complex analyic spaces. Using the theory so obtained, he proved the degeneration of l-adic weight spectral sequences over an arbitrary field. He also studied relations between log Hodge structures and log abelian varieties.
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