Sums of products of generalized Bernoulli polynomials

Kwang-Wu Chen

Vol. 208 (2003), No. 1, 39–52

DOI: 10.2140/pjm.2003.208.39

Abstract

In this paper, we investigate the zeta function

Z(P,χ,a,s)	= ∑ n1=1∞⋯∑ nr=1∞χ 1(n1)⋯χr(nr)
	⋅ P(n1 + a1,…,nr + ar)−s,

where a_i ≥ 0, χ_i is a Dirichlet character with conductor N_i, and P is a polynomial satisfying certain conditions. Its special values at nonpositive integers are closely related to generalized Bernoulli polynomials. Using this fact we can easily get sums of products of Euler polynomials and generalized Bernoulli polynomials.

Milestones

Received: 9 May 2001

Revised: 13 November 2001

Published: 1 January 2003