Fox functions and zeta-functions
| Project/Area Number |
21540029
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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 | Kinki University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
TSUKADA Haruo 近畿大学, 産業理工学部, 教授 (00257990)
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| Co-Investigator(Renkei-kenkyūsha) |
TANIGAWA Yoshio 名古屋大学, 大学院・多元数理科学研究科, 准教授 (50109261)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
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| Keywords | ゼータ関数 / 関数等式 / モジュラー関係式 / フーリエ級数 / 超幾何級数 / プラナ和公式 / 超幾何関数 / 短区間指標和 / エプシュタインゼータ関数 / アイゼンシュタインの等式 / オイラー積 / フリウィッツゼータ関数 / デデキンドイータ関数 / パーセヴァル等式 / フォックス関数 |
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| Research Abstract |
The purpose of the present research is to locate all the identities that have been assembled in the last 150 years after Riemann, equivalent to the functional equation for a wide class of zeta-functions in terms of Fox H-functions and by locating them in terms of the Meijer G-functions, to find new identities that are useful not only in mathematics but also in other scientific disciplines. In the year 2011, we were able to accomplish this task in the following setting : the origin of Plana's summation formula, the formula for short interval character sums and arithmetical Fourier series
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Report
(4 results)
Research Products
(47 results)
