On generalized Dedekind sums attached to Dirichlet characters
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)].
Dedekind-Petersson-Knopp-type identities
scientific article; zbMATH DE number 3877277