2011 Fiscal Year Final Research Report
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 |
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| Research Field |
Algebra
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| Research Institution | Ehime University |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2011
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| Keywords | ゼータ関数 / ゼータ正規化積 / ラプラシアンの行列式 |
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| 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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[Remarks] (1) Nobushige Kurokawa, Masato Wakayama Yoshinori Yamasaki, Milnor-Selberg zeta functions and zeta regularizations, submitted, 2012. MathArXiv : 1011. 3093
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[Remarks] (2) Yoshinori Yamasaki, Factorization formulas for higher depth determinants of the Laplacian on the n-sphere, submitted, 2012. MathArXiv : 1011. 3095
