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December 2019 A Generating Function to Generalize the Sum Formula for Quadruple Zeta Values
Tomoya MACHIDE
Tokyo J. Math. 42(2): 329-355 (December 2019). DOI: 10.3836/tjm/1502179282

Abstract

In the present paper, we prove an identity for the generating function of the quadruple zeta values with the action of the matrix ring $\mathrm{M}_{4}(\mathbb{Z})$. Taking homogeneous parts on both sides of the identity and substituting appropriate values for the variables, we obtain the sum formula for quadruple zeta values. We also obtain its weighted analogues, which include the formulas for this case proved by Guo and Xie (2009, J. Number Theory 129, 2747--2765) and by Ong, Eie, and Liaw (2013, Int. J. Number Theory 9, 1185--1198).

Citation

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Tomoya MACHIDE. "A Generating Function to Generalize the Sum Formula for Quadruple Zeta Values." Tokyo J. Math. 42 (2) 329 - 355, December 2019. https://doi.org/10.3836/tjm/1502179282

Information

Published: December 2019
First available in Project Euclid: 6 August 2018

zbMATH: 07209623
MathSciNet: MR4106582
Digital Object Identifier: 10.3836/tjm/1502179282

Subjects:
Primary: 11M32
Secondary: 16S34, 20C07

Rights: Copyright © 2019 Publication Committee for the Tokyo Journal of Mathematics

JOURNAL ARTICLE
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Vol.42 • No. 2 • December 2019
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