Multiple zeta values and zeta-functions of root systems

被引：4

作者：

Komori, Yasushi ^{[1
]}

Matsumoto, Kohji ^{[2
]}

Tsumura, Hirofumi ^{[3
]}

机构：

[1] Rikkyo Univ, Dept Math, Toshima Ku, Tokyo 1718501, Japan

[2] Nagoya Univ, Grad Sch Math, Chikusa Ku, Aichi 4648602, Japan

[3] Tokyo Metropolitan Univ, Dept Math & Informat Sci, Tokyo 1920397, Japan

来源：

PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES | 2011年 / 87卷 / 06期

关键词：

Multiple zeta-values; root systems; witten zeta-functions; BERNOULLI POLYNOMIALS;

D O I：

10.3792/pjaa.87.103

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We propose the viewpoint that the r-ple zeta-function of Euler-Zagier type can be regarded as a specialization of the zeta-function associated with the root system of C-r type. From this viewpoint, we can see that Zagier's well-known formula for multiple zeta values (MZVs) coincides with Witten's volume formula associated with a sub-root system of C-r type. Based on this observation, we generalize Zagier's formula and also give analogous results which correspond to a sub-root system of B-r type. We announce those results as well as some relevant results for partial multiple zeta values.

引用

页码：103 / 107

页数：5

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