Dept. Math, Hokkaido Univ. EPrints Server

An Elliptic Analogue of the Generalized Dedekind-Rademacher Sums

Preprint Series # 785
Machide, Tomoya An Elliptic Analogue of the Generalized Dedekind-Rademacher Sums. (2006);

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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.

Item Type:Preprint
Additional Information:20 copies, please. My recommender is Youichi Shibukawa.
Uncontrolled Keywords:Dedekind sums, Bernoulli functions
Subjects:11-xx NUMBER THEORY
ID Code:1537