We study many-term relations for multiple Dedekind sums including the case generalized by means of Dirichlet characters. We mainly use the method due to Carlitz. The main results contain the original reciprocity formula for Dedekind sums and its generalized formulas due to Apostol, Snyder and Carlitz.
Kazuhito Kozuka. "Multiple Dedekind sums attached to Dirichlet characters." Proc. Japan Acad. Ser. A Math. Sci. 83 (7) 104 - 108, July 2007. https://doi.org/10.3792/pjaa.83.104