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April 2020 A decomposition of $\zeta(2n+3)$ into sums of multiple zeta values
Minking Eie, Wen-Chin Liaw, Yao Lin Ong
Rocky Mountain J. Math. 50(2): 551-558 (April 2020). DOI: 10.1216/rmj.2020.50.551

Abstract

We evaluate the multiple zeta value ζ ( 1 , { 2 } n + 1 ) or its dual ζ ( { 2 } n , 3 ) . When n is even, along with stuffle relations already available, it is enough to evaluate all multiple zeta values of the form ζ ( { 2 } a , 3 , { 2 } b ) with a + b = n . Furthermore, we obtain a decomposition for 2 ζ ( 2 n + 3 ) as

ζ ( 3 , { 2 } n ) + ζ ( { 2 } n , 3 ) + r = 1 n | α | = n + 1 ζ ( 1 , 2 α 1 , 2 α 2 , , 2 α r ) ,

which also can be used to evaluate ζ ( { 2 } n , 3 ) when n is even.

Citation

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Minking Eie. Wen-Chin Liaw. Yao Lin Ong. "A decomposition of $\zeta(2n+3)$ into sums of multiple zeta values." Rocky Mountain J. Math. 50 (2) 551 - 558, April 2020. https://doi.org/10.1216/rmj.2020.50.551

Information

Received: 12 June 2019; Revised: 3 November 2019; Accepted: 4 November 2019; Published: April 2020
First available in Project Euclid: 29 May 2020

zbMATH: 07210978
MathSciNet: MR4104393
Digital Object Identifier: 10.1216/rmj.2020.50.551

Subjects:
Primary: 11M06
Secondary: 33E20, 40B05

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 2 • April 2020
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