KNOPP-TYPE IDENTITIES FOR GENERALIZED MULTIPLE DEDEKIND-TYPE SUMS

Abstract

In this paper, for any multivariable function with a periodicity and a certain distribution relation, we define a multiple Dedekind-type sum. Then by a combinatorialgeometric method, we study generalizations of Knopp's formula for the classical Dedekind sums. The main theorem contains many of the preceding results concerning generalizations of Knopp's formula.