An elliptic analogue of generalized Dedekind–Rademacher sums

Abstract: In this paper we introduce an elliptic analogue of the generalized Dedekind–Rademacher sums which satisfy reciprocity laws. In these sums, Kronecker''s double series play a role of elliptic Bernoulli functions. This paper gives an answer to the problem of S. Fukuhara and N. Yui concerning the elliptic Apostol–Dedekind sums. We also mention a relation between the generating function of Kronecker''s double series and that of the (Debye) elliptic polylogarithms studied by A. Levin. [Copyright &y& Elsevier]