2005 Fiscal Year Final Research Report Summary
Arithmetic of Automorphic Forms and Discrete Groups
| Project/Area Number |
16540013
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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 Professor, 大学院・理工学研究科, 助教授 (90166033)
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| Co-Investigator(Kenkyū-buntansha) |
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)
SHIGA Hriroshige Tokyo Institute of Technology, Graduate School of Science and Engineering, Professor, 大学院・理工学研究科, 教授 (10154189)
HATTORI Toshiaki Tokyo Institute of Technology, Graduate School of Science and Engineering, Associate Professor, 大学院・理工学研究科, 助教授 (30251599)
NAKAYAMA Chikara Tokyo Institute of Technology, Graduate School of Science and Engineering, Assistant, 大学院・理工学研究科, 助手 (70272664)
SOMEKAWA Mutsuro Tokyo Institute of Technology, Graduate School of Science and Engineering, Assistant, 大学院・理工学研究科, 助手 (70251600)
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| Project Period (FY) |
2004 – 2005
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| Keywords | Automorphic Forms / Discrete Groups / L-functions |
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| Research Abstract |
Mizumoto found that some congruences for Fourier coefficients of Siegel modular forms are preserved under the Eisenstein liftings of arbitrary degree. The proof is based on the integral representation due to Garrett and Boecherer for the Eisenstein series attached to cusp forms. In the course of investigation, he found also that such congruences give rise to congruences for the values at a critical point of corresponding standard L-functions. His recent research also shows that similar phenomena occur also in other types of liftings such as Shimura correspondences and the Ikeda liftings, and he hopes to treat such topics in future.
Kurokawa constructed and studied multi-trigonometric functions. In particular, he studied algebraicity and transcendency of their values. In connection with this topic, he also studied absolute tensor products, absolute differentiation, q-analogues of Mahler measures, and Selberg zeta functions.
Shiga investigated Teichmueller spaces of infinite dimension and mapping class groups. He studied the condition under which the action of the mapping class group becomes properly discontinuous.
Hattori studied applications of hyperbolic geometry to Diophantine equations.
Nakayama introduced analyitic etale site, and obtained the log Riemann-Hilbert correspondence with quasi-unipotent monodromy. He also proved its functoriality.
Somekawa constructed fundamental theory for the values of p-adic L-functions for algebraic varieties.
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