Derivatives of Dedekind sums and their reciprocity law. (Q1869795)
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scientific article; zbMATH DE number 1902880
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Derivatives of Dedekind sums and their reciprocity law. |
scientific article; zbMATH DE number 1902880 |
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Derivatives of Dedekind sums and their reciprocity law. (English)
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28 April 2003
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The author evaluates Barnes' double zeta function at the negative integers in two ways, one in terms of Bernoulli numbers, and another as a finite sum of Hurwitz zeta functions. Equating these expressions leads to a new and interesting proof of the reviewer's reciprocity law for generalized Dedekind sums. More general results are indicated as being obtainable from Barnes' multiple zeta functions.
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Derivatives of Dedekind sums
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reciprocity law
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Barnes' multiple zeta function
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Stirling modular form
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double gamma function
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