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arXiv · 2610.39075

Reciprocity formulas for generalized Dedekind character sums

Yuan He
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Abstract

In this paper, we apply the Fourier series technique to establish a new formula for the product of the generalized Bernoulli function and the Bernoulli function. As applications, we derive some reciprocity formulas for generalized Dedekind character sums. In particular, we show that the reciprocity formulas of Berndt, Can, and others follow as special cases.

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Yuan He. 2026-10-29. Reciprocity formulas for generalized Dedekind character sums. https://arxiv.org/abs/2610.39075

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