An elliptic analogue of generalized Dedekind–Rademacher sums

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• 作者：Tomoya Machide
• 关键词：Dedekind sums ; Generalized Dedekind– ; Rademacher sums ; Reciprocity laws ; Elliptic analogue ; Kronecker's double series ; Elliptic Apostol– ; Dedekind sums
• 刊名：Journal of Number Theory
• 出版年：2008
• 出版时间：April 2008
• 年：2008
• 卷：128
• 期：4
• 页码：1060-1073
• 全文大小：157 K

文摘

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.