Alternating Euler sums at the negative integers
Number Theory
2016-10-10 v1
Abstract
We study three special Dirichlet series, two of them alternating, related to the Riemann zeta function. These series are shown to have extensions to the entire complex plane and we find their values at the negative integers (or residues at poles). These values are given in terms of Bernoulli and Euler numbers.
Cite
@article{arxiv.0811.4437,
title = {Alternating Euler sums at the negative integers},
author = {Khristo N. Boyadzhiev and H. Gopalkrishna Gadiyar and R. Padma},
journal= {arXiv preprint arXiv:0811.4437},
year = {2016}
}
Comments
15 pages, To appear in the Hardy-Ramanujan journal