Reciprocity formulas for certain generalized Hardy-Berndt sums (2401.00774v5)

Abstract: In this paper, we establish some reciprocity formulas for certain generalized Hardy-Berndt sums by using the Fourier series technique and some properties of the periodic zeta function and the Lerch zeta function. It turns out that one of Hardy's reciprocity theorems is deduced as a special case.