A study on multiple zeta function and zeta regularized products
Project/Area Number |
21740019
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Single-year Grants |
Research Field |
Algebra
|
Research Institution | Ehime University |
Principal Investigator |
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Project Period (FY) |
2009 – 2011
|
Project Status |
Completed (Fiscal Year 2011)
|
Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
|
Keywords | ゼータ関数 / ゼータ正規化積 / ラプラシアンの行列式 |
Research Abstract |
We introduced" higher depth zeta regularized products" as generalizations of the usual regularized products and have studied their analytic and algebraic properties. In particular, we have obtained explicit expressions of" higher depth determinants" of the Laplacian on some manifolds. Moreover, we also introduced" Schur multiple zeta functions" as extensions of the Euler-Zagier multiple zeta functions. Several fundamental properties and combinatorial formulas for the zeta functions have been obtained or expected.
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Report
(4 results)
Research Products
(38 results)