多重交替zeta值的恒等式

沈忠燕, 蔡天新

数学学报 ›› 2013, Vol. 56 ›› Issue (4) : 441-450.

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数学学报 ›› 2013, Vol. 56 ›› Issue (4) : 441-450. DOI: 10.12386/A2013sxxb0045
论文

多重交替zeta值的恒等式

    沈忠燕1, 蔡天新2
作者信息 +

Some Identities for Alternating Multiple Zeta Values

    Zhong Yan SHEN1, Tian Xin CAI2
Author information +
文章历史 +

摘要

利用调和乘积公式,得到了以下恒等式
.

Abstract

In this note, using harmonic shuffle relation, we obtain the following identities,
.

关键词

多重交替zeta值 / 调和乘积公式 / 恒等式

Key words

multiple alternating zeta values / harmonic shuffle relation / identity

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沈忠燕, 蔡天新. 多重交替zeta值的恒等式. 数学学报, 2013, 56(4): 441-450 https://doi.org/10.12386/A2013sxxb0045
Zhong Yan SHEN, Tian Xin CAI. Some Identities for Alternating Multiple Zeta Values. Acta Mathematica Sinica, Chinese Series, 2013, 56(4): 441-450 https://doi.org/10.12386/A2013sxxb0045

参考文献

[1] Gangl H., Kaneko M., Zagier D., Double Zeta Values and Modular Forms (S. Böcherer. ed.), Proceedings of the Conference in Memory of Tsuneo Arakawa: Automorphic Forms and Zeta Functions, World Scientific, Singapore, 2006: 71-106.

[2] Nakamura T., Restricted and weighted sum formulas for double zeta values of even weight, Šiauliai Math. Semin., 2009, 12: 151-155.

[3] Sankaranaryanan A., An identities involving Riemann zeta function, Indian J. Pure Appl. Math., 1987, 18: 794-800.

[4] Shen Z. Y., Cai T. X., Some identities for multiple zeta values, J. Number Theory, 2012, 132: 314-323.

[5] Sitaramachandrarao R., Davis B., Some identities involving the Riemann zeta function (II), Indian J. Pure Appl. Math., 1986, 17: 1175-1186.

基金

国家自然科学基金资助项目(10871169);浙江省自然科学基金资助项目(LQ13A010012);浙江外国语学院重点课题资助项目(2012Z07)

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