Weighted sum formula for multiple zeta values

Li Guo; Bingyong Xie

doi:10.1016/j.jnt.2009.04.018

Weighted sum formula for multiple zeta values

Li Guo, Bingyong Xie

Research output: Contribution to journal › Article › peer-review

32 Scopus citations

Abstract

The sum formula is a basic identity of multiple zeta values that expresses a Riemann zeta value as a homogeneous sum of multiple zeta values of a given dimension. This formula was already known to Euler in the dimension two case, conjectured in the early 1990s for higher dimensions and then proved by Granville and Zagier. Recently a weighted form of Euler's formula was obtained by Ohno and Zudilin. We generalize it to a weighted sum formula for multiple zeta values of all dimensions.

Original language	English
Pages (from-to)	2747-2765
Number of pages	19
Journal	Journal of Number Theory
Volume	129
Issue number	11
DOIs	https://doi.org/10.1016/j.jnt.2009.04.018
State	Published - Nov 2009
Externally published	Yes

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10.1016/j.jnt.2009.04.018

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title = "Weighted sum formula for multiple zeta values",

abstract = "The sum formula is a basic identity of multiple zeta values that expresses a Riemann zeta value as a homogeneous sum of multiple zeta values of a given dimension. This formula was already known to Euler in the dimension two case, conjectured in the early 1990s for higher dimensions and then proved by Granville and Zagier. Recently a weighted form of Euler's formula was obtained by Ohno and Zudilin. We generalize it to a weighted sum formula for multiple zeta values of all dimensions.",

author = "Li Guo and Bingyong Xie",

year = "2009",

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AB - The sum formula is a basic identity of multiple zeta values that expresses a Riemann zeta value as a homogeneous sum of multiple zeta values of a given dimension. This formula was already known to Euler in the dimension two case, conjectured in the early 1990s for higher dimensions and then proved by Granville and Zagier. Recently a weighted form of Euler's formula was obtained by Ohno and Zudilin. We generalize it to a weighted sum formula for multiple zeta values of all dimensions.

UR - https://www.scopus.com/pages/publications/68549122522

U2 - 10.1016/j.jnt.2009.04.018

DO - 10.1016/j.jnt.2009.04.018

M3 - 文章

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SN - 0022-314X

VL - 129

SP - 2747

EP - 2765

JO - Journal of Number Theory

JF - Journal of Number Theory

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ER -

Weighted sum formula for multiple zeta values

Abstract

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