A generalization of gamma functions and Kronecker's limit formulas |
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Authors: | Koji Katayama |
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Institution: | Department of Mathematics, Tsuda College, Kodaira, Tokyo, Japan |
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Abstract: | We obtain a “Kronecker limit formula” for the Epstein zeta function. This is done by introducing a generalized gamma function attached to the Epstein zeta function. The methods involve generalizing ideas of Shintani and Stark. We first show that a generalized gamma function appears as the value at s=0 of the first derivative of the associated Epstein zeta function. Then this is used to yield Kronecker's limit formula and its “s=0”-version. |
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Keywords: | 11R42 11M35 33B15 |
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