2003 Fiscal Year Final Research Report Summary
Research on Eisenstein series
| Project/Area Number |
14540013
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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) |
TSUJI Hajime Sophia University, Faculty of Science and Engineering, Professor, 理工学部, 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, Associate Professor, 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 Professor, 大学院・理工学研究科, 助教授 (30251599)
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| Project Period (FY) |
2002 – 2003
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| Keywords | Eisenstein series / Automorphic forms / Discerete groups |
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| Research Abstract |
Mizumoto found a new type of series associated to 2n number of elliptic modular forms. This series involves a new special function expressed as an integral of products of modified Bessel functions, and has analytic continuation and functional equation. Such series have not been investigated so far, and they deserve careful study.
Kurokawa constructed and studied multi-trigonomotric functions. Further he studied q-analogues of multi-trigonometric functions, absolute tensor products, absolute differentiation, and spectra of categories.
Shiga investigated the behavior of the solutions of the first boundary value problem (Dirichlet problem) for continuous functions on boundaries of bordered Riemann surfaces ; he showed real analyticity of the solutions with respect to the parameters.
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