Derivatives of Dedekind sums and their reciprocity law |
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Authors: | Kaori Ota |
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Affiliation: | Department of Mathematics & Computer Science, Tsuda College, 2-1-1 Tsuda-cho, Kodaira-shi, Tokyo 187-8577, Japan |
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Abstract: | In this paper derivatives of Dedekind sums are defined, and their reciprocity laws are proved. They are obtained from values at non-positive integers of the first derivatives of Barnes’ double zeta functions. As special cases, they give finite product expressions of the Stirling modular form and the double gamma function at positive rational numbers. |
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Keywords: | Derivatives of Dedekind sums Reciprocity law Barnes&rsquo multiple zeta function Stirling modular form Double gamma function |
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