ON WITTEN MULTIPLE ZETA-FUNCTIONS ASSOCIATED WITH SEMI-SIMPLE LIE ALGEBRAS IV
ON WITTEN MULTIPLE ZETA-FUNCTIONS ASSOCIATED WITH SEMI-SIMPLE LIE ALGEBRAS IV
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DOI：
10.1007/978-0-8176-8334-4_11
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发表时间：
2009-07
影响因子：
0.5
通讯作者：
Y. Komori;Kohji Matsumoto;Hirofumi Tsumura
中科院分区：
文献类型：
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作者：
Y. Komori;Kohji Matsumoto;Hirofumi Tsumura
我们证明了Witten多元Zeta函数(或根系统的Zeta函数)之间函数关系的某些一般形式。这些函数关系的结构背景是由关于Weyl群的对称性给出的。根据这些关系，我们可以推导出Witten Zeta-函数在正偶数处的值的显式表达式，这些值是用根系的广义Bernoulli数表示的。此外，我们还引入了根系统Bernoulli数的母函数，利用它可以给出一个计算根系统Bernoulli数的算法。
We prove certain general forms of functional relations among Witten multiple zeta-functions in several variables (or zeta-functions of root systems). The structural background of these functional relations is given by the symmetry with respect to Weyl groups. From these relations, we can deduce explicit expressions of values of Witten zeta-functions at positive even integers, which are written in terms of generalized Bernoulli numbers of root systems. Furthermore, we introduce generating functions of Bernoulli numbers of root systems, using which we can give an algorithm of calculating Bernoulli numbers of root systems.