| Project/Area Number |
18540018
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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 |
KUROKAWA Nobushige Tokyo Institute of Technology, Graduate School of Science, Professor (70114866)
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| Co-Investigator(Kenkyū-buntansha) |
MIMACHI Katsuhisa Tokyo Institute of Technology, Graduate School of Science, Professor (40211594)
MIZUMOTO Shin-ichiro Tokyo Institute of Technology, Graduate School of Science, Associate Professor (90166033)
SATOH Takakazu Tokyo Institute of Technology, Graduate School of Science, Associate Professor (70215797)
WAKAYAMA Masato Kyushu University, Graduate School of Mathematics, Professor (40201149)
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| Project Period (FY) |
2006 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥4,010,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥510,000)
Fiscal Year 2007: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2006: ¥1,800,000 (Direct Cost: ¥1,800,000)
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| Keywords | multiple sine function / zeta function / Kinkelin formula / Jackson integral / Casimir energy / Mahler measure / Euler integral / Jackson-Mellin transform / 代数性 / 超越性 / 量子化 / カタラン定数 / 多重ガンマ関数 |
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| Research Abstract |
We studied zeta functions and multiple sine functions extending the theory of usual siine function. Then, we established their fundamental properties. Especially we studied special values of zeta functions via multiple sine functions. This includes the study of quantum deformations of the Catalan constant Moreover, we studied the following themes: Kinkelin formula for multiple sine functions, Casimir energies on the infinite symmetric group, Jackson integral analogue of Euler integral, generalized Mahler measures, and Jackson-Mellin transforms as quantizations of zeta functions.
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