Degenerate and character Dedekind sums Original Research Article

In this paper, we study on two subjects. We first construct degenerate analogues of Dedekind sums in the sense of Apostol, Carlitz and Takács, and prove the corresponding reciprocity formulas. Secondly, we define generalized Dedekind character sums, which are explicit extensions of Berndtʹs definition, and prove the reciprocity laws. From the derived reciprocity laws, we obtain Berndtʹs reciprocity laws as special cases.