A combinatorial-geometric viewpoint of Knopp's formula for Dedekind sums

Abstract

In this paper, by means of a combinatorial-geometric method, we give a new proof of Knopp's formula for Dedekind sums and its generalizations to multiple Dedekind sums attached to Dirichlet characters. The combinatorial-geometric method for studying Dedekind sums were introduced by Beck, who proved the well-known reciprocity formula for Dedekind sums and some of its generalizations by the method. The motive of this paper is to find a similar approch to Knopp's formula .