Finite Multiple zeta Values and Finite Euler Sums
Number Theory
2015-11-30 v4
Abstract
The alternating multiple harmonic sums are partial sums of the infinite series defining the Euler sums which are the alternating version of the multiple zeta value series. In this paper, we present some systematic structural results of the van Hamme type congruences of these sums, collected as finite Euler sums. Moreover, we relate this to the structure of the Euler sums, which generalizes the corresponding result of the multiple zeta values. We also provide a few conjectures with extensive numerical support.
Cite
@article{arxiv.1507.04917,
title = {Finite Multiple zeta Values and Finite Euler Sums},
author = {Jianqiang Zhao},
journal= {arXiv preprint arXiv:1507.04917},
year = {2015}
}
Comments
A new Conjecture 9.7 is added while the first theorem in section 10 was removed