Dept. Math, Hokkaido Univ. EPrints Server

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

Preprint Series # 863
Machide, Tomoya Elliptic Dedekind-Rademacher Sums and Transformation Formulae of Certain Infinite Series. (2007);

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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.

Item Type:Preprint
Additional Information:Please 10 copies. My recommender is SHIBUKAWA Youichi.
Uncontrolled Keywords:Generalized Dedekind sums, elliptic Dedekind sums, Transformation formulae, Kronecker's double series, modular forms, reciprocity formulae.
Subjects:11-xx NUMBER THEORY
ID Code:1717