On a recent reciprocity formula for Dedekind sums

Abstract

Let [Formula: see text] denote the classical Dedekind sum and [Formula: see text]. Recently, Du and Zhang proved the following reciprocity formula. If [Formula: see text] and [Formula: see text] are odd natural numbers, [Formula: see text], then [Formula: see text] where [Formula: see text] and [Formula: see text]. In this paper, we show that this formula is a special case of a series of similar reciprocity formulas. Whereas Du and Zhang worked with the connection of Dedekind sums and values of [Formula: see text]-series, our main tool is the three-term relation for Dedekind sums.