Multiple Dedekind Type Sums and Their Related Zeta Functions

Abstract

The main purpose of this paper is to use the multiple twisted Bernoulli polynomials and their interpolation functions to construct multiple twisted Dedekind type sums. We investigate some properties of these sums. By use of the properties of multiple twisted zeta functions and the Bernoulli functions involving the Bernoulli polynomials, we derive reciprocity laws of these sums. Further developments and observations on these new Dedekind type sums are given.

Keywords

• twisted (<i>h</i>,<i>q</i>)-Bernoulli numbers and polynomials
• Barnes’ type multiple zeta function
• higher-order Bernoulli numbers and polynomials
• Dedekind sums
• reciprocity law