交错Mordell-Tornheim和Witten多重级数

Alternating Mordell-Tornheim and Witten multiple series

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摘要本文通过对几个交错多重调和级数的讨论,统一地得到了交错Mordell-Tornheim和Witten多重级数的一些已有的和新的表达式. In this note, we obtain some known and new evaluation formulae on alternating Mordell-Tornheim and Witten multiple series via several alternating multiple harmonic series.

作者夏彬 蔡天新

机构地区北京大学数学科学学院浙江大学数学系

出处《中国科学：数学》 CSCD 北大核心 2010年第6期517-532,共16页 Scientia Sinica：Mathematica

基金国家自然科学基金(批准号:10871169)资助项目

关键词交错多重调和级数 Mordell—Tornheim多重级数 RIEMANN zeta值 Witten多重级数 alternating multiple harmonic series, Mordell-Tornheim multiple series, Riemann zeta values, Witten multiple series

分类号 O173 [理学—基础数学]

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1Tornheim L. Harmonic double series. Amer J Math, 1950, 72:303-314.
2Subbarao M V, Sitaramachandrarao R. On some infinite series of L. J. Modell and their analogues. Pacific J Math, 1985, 119:245 255.
3Matsumoto K. On the analytic contiuation of various multiple zeta-function. In: Bennett M A, et al. eds. Number Theory for the Millennium, vol. II. Proceedings of Millennial Conference on Number Theory. Wellesley: A K Peters, 2002, 417-440.
4Matsumoto K. On Mordell-Tornheim and other multiple zeta-function. In: Heath-Brown D R, Moroz B Z, eds. Proceedings of the Session in Analytic Number Theory and Diophantine Equations. Bonner Math Schriften, vol. 360. Bonn: Univ Bonn, 2003.
5Huard J G, Williams K S, Zhang N Y. On Tornheim's double series. Acta Arith, 1996, 75:105- 117.
6Matsumoto K, Nakamura T, Oehiai H, et al. On value-relations, functional relations and singularities of Mordell. Tornheim and related triple zeta~functions. Acta Arith, 2008, 132:99-125.
7Tsumura H. On Mordell-Tornheim zeta-values. Proc Amer Math Soc, 2005, 133:2387-2393.
8Zagier D. Values of zeta functions and their applications. In: Proc First Congress of Math, vol. II. Progress in Math, vol. 120. Boston: Birkhauser, 1994, 497- 512.
9Matsumoto K, Tsumura H. On Witten multiple zeta-functions associated with semisimple Lie Algebras I. Ann Inst Fourier (Grenoble), 2006, 56:1457-1504.
10Nakamura T. Double Lerch value relations and functional relations for Witten zeta functions. Tokyo J Math, 2008, 31:551-574.

1吴云飞.一类涉及Riemann zeta函数的积分值[J].宁波大学学报（理工版）,2001,14(4):61-63.
2Zhong Yan SHEN,Tian Xin CAI.Some Weighted Sum Identities for Double Zeta Values[J].Acta Mathematica Sinica,English Series,2016,32(7):797-806.
3雷鹏,郭锂.多重Zeta偶数值的六重求和公式(英文)[J].兰州大学学报（自然科学版）,2013,49(1):100-102. 被引量：1
4王元.王元院士致本刊的一封信[J].高等数学研究,2011,14(3):10-10.
5沈忠燕,蔡天新.多重交替zeta值的恒等式[J].数学学报（中文版）,2013,56(4):441-450.
6王元.均匀设计──一种试验设计方法[J].科技导报,1994,12(5):20-21. 被引量：23
7庆祝蒋锡夔院士八十华诞学术论文专辑征稿启示[J].化学学报,2006,64(5).
8庆祝蒋锡夔院士八十华诞学术论文专辑征稿启示[J].化学学报,2006,64(7).
9庆祝蒋锡夔院士八十华诞学术论文专辑征稿启示[J].化学学报,2006,64(2).
10庆祝蒋锡夔院士八十华诞学术论文专辑征稿启示[J].化学学报,2006,64(4).

中国科学：数学

2010年第6期

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交错Mordell-Tornheim和Witten多重级数

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