2013 Fiscal Year Final Research Report
Research on arithmetic and geometric properties of multiple higher Mahler measures
| Project/Area Number |
23740036
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Osaka University of Health and Sport Sciences (2012-2013)
Kinki University (2011) |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2013
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| Keywords | Mahler測度 / L関数 / ゼータMahler測度 / ポリログ関数 / 多重ゼータ値 / 多重L値 |
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| Research Abstract |
We showed relations between multiple L values and multiple higher Mahler measures by applying algebraic properties of multiple polylogarithms. From the view point of the generating function of multiple higher Mahler measure (zeta Mahler measure), we also found linear relations between multiple zeta values and multiple higher Mahler measures, and explicit formulas of multiple higher Mahler measures.
We generalized Dirichlet L-functions based on the construction of Arakawa-Kaneko's zeta function and showed the relation between such generalized L-functions and multiple L values. We introduced poly-Euler numbers via special values of such generalized L-function, and investigated some properties of poly-Euler numbers. In particular, we obtained number theoretic properties and combinatorial interpretations of poly-Euler numbers.
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Research Products
(25 results)
