Arithmetical properties of double Möbius-Bernoulli numbers

Abstract

Given positive integers n, n′ and k, we investigate the Möbius-Bernoulli numbers Mk(n), double Möbius-Bernoulli numbers Mk(n,n′), and Möbius-Bernoulli polynomials Mk(n)(x). We find new identities involving double Möbius-Bernoulli, Barnes-Bernoulli numbers and Dedekind sums. In part of this paper, the Möbius-Bernoulli polynomials Mk(n)(x), can be interpreted as critical values of the following Dirichlet type L-function

Keywords

• möbius-bernoulli numbers
• barnes-bernoulli numbers
• dedekind sums
• 11a05
• 33e99