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

^*此作品的通讯作者

科研成果: 期刊稿件 › 文章 › 同行评审

32 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	2747-2765
页数	19
期刊	Journal of Number Theory
卷	129
期	11
DOI	https://doi.org/10.1016/j.jnt.2009.04.018
出版状态	已出版 - 11月 2009
已对外发布	是

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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

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M3 - 文章

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Weighted sum formula for multiple zeta values

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