Document Type

Article

Publication Date

2-2013

Publication Title

Forum Mathematicum

DOI

10.1515/forum-2012-0144

Abstract

Let s1,⋯,sd be d positive integers and define the multiple t-values of depth d byt(s1,⋯,sd)=∑n1>⋯>nd≥11(2n1−1)s1⋯(2nd−1)sd,which is equal to the multiple Hurwitz-zeta value 2−wζ(s1,⋯,sd;−12,⋯,−12) where w=s1+⋯+sd is called the weight. For d≤n, let T(2n,d) be the sum of all multiple t-values with even arguments whose weight is 2n and whose depth is d. In 2011, Shen and Cai gave formulas for T(2n,d) for d≤5 in terms of t(2n), t(2)t(2n−2) and t(4)t(2n−4). In this short note we generalize their results to arbitrary depth by using the theory of symmetric functions established by Hoffman (2012).

Comments

This version of the paper was obtained from arXIV.org. In order for the work to be deposited in arXIV.org, the authors must hold the rights or the work must be under Creative Commons Attribution license, Creative Commons Attribution-Noncommercial-ShareAlike license, or Create Commons Public Domain Declaration. The publisher's final edited version of this article is available at Forum Mathematicum.

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