An Elliptic Analogue of the Generalized Dedekind-Rademacher Sums
Preprint Series # 785
Machide, Tomoya An Elliptic Analogue of the Generalized Dedekind-Rademacher Sums. (2006);
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.
|Additional Information:||20 copies, please.
My recommender is Youichi Shibukawa.|
|Uncontrolled Keywords:||Dedekind sums, Bernoulli functions|
|Subjects:||11-xx NUMBER THEORY|