On generalized Dedekind sums attached to Dirichlet characters
type: Item
instance of: scholarly article
title: On generalized Dedekind sums attached to Dirichlet characters
zbMATH Open document ID: 0551.10022
DOI: 10.1016/0022-314X(84)90078-7
author: Chiaki Nagasaka
published in: Journal of Number Theory
publication date: 1984-01-01T00:00:00Z
review text: The author derives reciprocity formulas and Dedekind-Petersson-Knopp-type identities for generalized Dedekind sums associated with Dirichlet characters and certain congruence subgroups of the modular group. The generalized Dedekind sums occur in the transformation laws of functions considered in earlier work of \textit{L. J. Goldstein} and \textit{M. Razar} [Nagoya Math. J. 63, 93-121 (1976; Zbl 0346.10011)] and of the author [Mem. Fac. Sci., Kyushu Univ., Ser. A 37, 35-43 (1983; Zbl 0512.10030)]. The formulas are also recast as transformational and eigen properties of Hecke-type operators, using the method of \textit{L. A. Parson} and \textit{K. H. Rosen} [Math. Scand. 49, 5-14 (1981; Zbl 0472.10017)].
Mathematics Subject Classification ID: 11F03
Mathematics Subject Classification ID: 11B39
zbMATH DE Number: 3877277
zbMATH Keywords: reciprocity formulas
zbMATH Keywords: Dedekind-Petersson-Knopp-type identities
zbMATH Keywords: generalized Dedekind sums
zbMATH Keywords: congruence subgroups
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3877277