On a recent reciprocity formula for Dedekind sums

摘要

Let s(a, b) denote the classical Dedekind sum and S(a, b) = 12s(a, b). Recently, Du and Zhang proved the following reciprocity formula. If a and b are odd natural numbers, (a, b) = 1, thenS(2a*, b) + S(2b*, a) = a(2)+b(2)+4/2ab - 3,where aa* (math) 1 mod b and bb* (math) 1 mod a. 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 L-series, our main tool is the three-term relation for Dedekind sums.