Elliptic Dedekind-Rademacher Sums and Transformation Formulae of Certain Infinite Series

Abstract

We give a transformation formula for certain infinite series in which some elliptic Dedekind-Rademacher sums arise. In the course of its proof, we also obtain a transformation formula for elliptic Dedekind-Rademacher sums. When a complex parameter $¥tau$ tends to $i ¥infty$, these represent some classical results which include the reciprocity formula for Apostol-Dedekind sums