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

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 Title: Elliptic Dedekind-Rademacher Sums and Transformation Formulae of Certain Infinite Series Authors: Machide, Tomoya Browse this author Keywords: Generalized Dedekind sums elliptic Dedekind sums Transformation formulae Kronecker's double series modular forms reciprocity formulae Issue Date: 2007 Publisher: Department of Mathematics, Hokkaido University Journal Title: Hokkaido University Preprint Series in Mathematics Volume: 863 Start Page: 1 End Page: 22 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. Type: bulletin (article) URI: http://hdl.handle.net/2115/69672 Appears in Collections: 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics