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arXiv · 2401.00774

Reciprocity formulas for certain generalized Hardy-Berndt sums

Yuan He
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Abstract

In this paper, we introduce the generalized Hardy-Berndt sums. We establish some formulas of products of the Bernoulli and Euler functions by using the Fourier series technique and some properties of the periodic-zeta and Lerch-zeta functions. As applications of the results, we give some reciprocity formulas for the generalized Hardy-Berndt sums. It turns out that Hardy's reciprocity formulas follow as special cases and that Goldberg's three-term reciprocity formulas are recovered.

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Yuan He. 2024-01-01. Reciprocity formulas for certain generalized Hardy-Berndt sums. https://arxiv.org/abs/2401.00774

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