2024-03-28T12:04:10Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/696722022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Elliptic Dedekind-Rademacher Sums and Transformation Formulae of Certain Infinite SeriesMachide, Tomoyaopen accessGeneralized Dedekind sumselliptic Dedekind sumsTransformation formulaeKronecker's double seriesmodular formsreciprocity formulae410We 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.Department of Mathematics, Hokkaido University2007engdepartmental bulletin paperVoRhttps://doi.org/10.14943/84013http://hdl.handle.net/2115/6967210.14943/84013Hokkaido University Preprint Series in Mathematics863122https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69672/1/pre863.pdfapplication/pdf190.21 KB2007