Document Type

Article

Publication Date

5-2015

Publication Title

International Journal of Number Theory

DOI

10.1142/S1793042115500530

Abstract

Euler's sum formula and its multi-variable and weighted generalizations form a large class of the identities of multiple zeta values. In this paper, we prove a family of identities involving Bernoulli numbers and apply them to obtain infinitely many weighted sum formulas for double zeta values and triple zeta values where the weight coefficients are given by symmetric polynomials. We give a general conjecture in arbitrary depth at the end of the paper.

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 International Journal of Number Theory.

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