Reciprocity formulas for certain generalized Hardy-Berndt sums
arXiv:2401.00774
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.
31 pages