Restricted Sum Formula of Multiple Zeta Values
Number Theory
2018-04-06 v1
Abstract
Let Q(4n,d) be the sum of all multiple zeta values of depth d and weight 4n whose arguments are all multiples of 4. In this paper we derive a formula of Q(4n,d) for all d>2 as a finite sum involving binomial coefficients, Bernoulli numbers and the quantities Q(4m,2). The number of terms is about 3d^2/8 which is independent of n.
Cite
@article{arxiv.1303.3607,
title = {Restricted Sum Formula of Multiple Zeta Values},
author = {Haiping Yuan and Jianqiang Zhao},
journal= {arXiv preprint arXiv:1303.3607},
year = {2018}
}
Comments
8 pages