2024-03-28T09:56:57Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/695932022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116An Elliptic Analogue of the Generalized Dedekind-Rademacher SumsMachide, TomoyaDedekind sumsBernoulli functions410In 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.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69593info:doi/10.14943/83935https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69593/1/pre785.pdfHokkaido University Preprint Series in Mathematics7851122006engpublisher