A study of zeta functions of prehomogeneous vector spaces and multiple zeta values
| Project/Area Number |
20540033
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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 |
OHNO Yasuo Kinki University, 理工学部, 教授 (70330230)
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| Co-Investigator(Renkei-kenkyūsha) |
WAKATSUKI Satoshi 金沢大学, 数物科学系, 助教 (10432121)
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 数論 / 概均質ベクトル空間 / ゼータ関数 / 多重ゼータ値 / 特殊値 / 2元3次形式 / 類数 / ポリログ / 超幾何関数 / 超幾何微分方程式 / 一般超幾何関数 / ベルヌーイ数 |
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| Research Abstract |
We figured out algebraic relations among the zeta functions of the prehomogeneous vector space associated with binary cubic forms with all lattices over the integer ring. These relations suggest the existence of beautiful symmetries of these objects, which are not yet known. We also clarified the relation among multiple zeta values and multiple zeta-star values, and figured out the explicit formula of Riemann zeta values of positive integral points in terms of multiple zeta-star analogue of Michael Hoffman's conjectural basis. Moreover we obtain a generating function representation of totals of multiple zeta-star values of fixed weight, depth and i-heights in terms of generalized hypergeometric functions. We also gave a kind of duality formula for multiple zeta-star values of height one. Farther we obtained another generalization of sum formula for multiple zeta values and many related results. These results are important for understanding the structure of Q-algebra spanned by all multiple zeta values.
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Report
(4 results)
Research Products
(42 results)
