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An Elliptic Analogue of the Generalized Dedekind-Rademacher Sums
| Title: | An Elliptic Analogue of the Generalized Dedekind-Rademacher Sums |
| Authors: | Machide, Tomoya Browse this author |
| Keywords: | Dedekind sums | | Bernoulli functions |
| Issue Date: | 2006 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 785 |
| Start Page: | 1 |
| End Page: | 12 |
| Abstract: | 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. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69593 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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