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arXiv · 2512.20542

Reciprocity For Dedekind Sums via Conical Zeta Values

Yerko Torres-Nova
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Abstract

We study reciprocity formulas for Dedekind sums associated with absolutely continuous functions, extending the classical Dedekind-Rademacher reciprocity formula. In particular, we treat the case of periodic Bernoulli functions. Our approach generalizes an integral method and uses Fourier analysis to show that the reciprocity for polynomial-type functions admits a geometric interpretation in terms of conical zeta values.

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Yerko Torres-Nova. 2025-12-23. Reciprocity For Dedekind Sums via Conical Zeta Values. https://arxiv.org/abs/2512.20542

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