| Project/Area Number |
11440010
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Kyushu University |
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Principal Investigator |
WAKAYAMA Masato Faculty of Mathematics, Professor, 大学院・数理学研究院, 教授 (40201149)
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| Co-Investigator(Kenkyū-buntansha) |
OCHIAI Hiroyuki Nagoya University, Graduate School of Mathematics, Associate Professor, 大学院・多元数理科学研究科, 助教授 (90214163)
KUROKAWA Nobushige Tokyo Institute of Technology, Department of Mathematics, Professor, 大学院・理工学研究科, 教授 (70114866)
今野 拓也 九州大学, 大学院・数理学研究院, 助教授 (00274431)
金子 昌信 九州大学, 大学院・数理学研究院, 教授 (70202017)
吉田 正章 九州大学, 大学院・数理学研究院, 教授 (30030787)
三町 勝久 東京工業大学, 大学院・理工学研究科, 教授 (40211594)
三鳥川 寿一 津田塾大学, 学芸学部, 教授 (80055318)
梅田 亨 京都大学, 大学院・理学研究科, 助教授 (00176728)
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| Project Period (FY) |
1999 – 2002
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| Project Status |
Completed (Fiscal Year 2002)
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| Budget Amount *help |
¥14,200,000 (Direct Cost: ¥14,200,000)
Fiscal Year 2002: ¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2001: ¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2000: ¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 1999: ¥4,100,000 (Direct Cost: ¥4,100,000)
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| Keywords | zeta regularized product / trace formula / Selberg zeta function / specter zeta function / non-commutative harmonicoscillator / q-analogue / determinant expression / Riemann zeta function / リーマンゼータ / セルバーグゼータ / オイラー定義 / 関数等式 / 局所対称空間 / カシミール効果 / パフィアン / 表現論 / セルバーグ・ゼータ関数 / Pfaffian / Capelli恒等式 / 不変微分作用素 / ホロノミー |
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| Research Abstract |
The purpose of this research project was to make a detailed study of dualities -- " infinite sum=infinite product" type identities and representations from the trace formulas point of views.
During the period we obtained the following results :
1) The higher and ordinary analogue of the Euler constants for the Dedekind and Selberg zeta functions (+ Kurokawa, Iijima, Hashimoto)
2) Zeta regularized products and the determinant expressions of several zeta functions : a) a generalization of Lerch's formula to higher degree polynomials, b) Introducing a new notion called Donburi product and we
established a q-analogue of Lerch' s formulas. C) Calculating several sine functions for rings and also their q-analogue (Kurokawa, Ochiai, Kimoto, Muller-Stuler, Sonoki)
3) We found the nice q-analogue of the Riemann zeta function and calculated the special values (+Kurokawa, Kaneko)
4) We made a description of the specter of the non-commutative harmonic oscillators and study the spectral zeta function (+A.Parmeggiani, Nagatou, Nakao, Ichinose)
5) We introduced and studied about the zeta extensions, especially, investigated the higher Selberg and Riemann zeta functions (+Kurokawa, Matsuda)
6) We studied the absolute derivations and gave some conjecture of the determinant expression (+Kurokawa, Ochiai)
7) Multiple sine functions theory was developed (+Kurokawa, Ochiai)
8) We established the explicit formula of the Capelli identity for the skew symmetric matrices (+Kinoshita)
9) A density theorem for the holonomy groups was established (+ Kimoto)
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