Zeta and L-functions and Bernoulli polynomials of root systems
Zeta and L-functions and Bernoulli polynomials of root systems
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DOI：
10.3792/pjaa.84.57
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发表时间：
2008-05
影响因子：
2.3
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
这篇文章基本上是作者的论文（7，8，9，10）的公告，尽管有些例子没有包括在这些论文中。我们认为什么是所谓的zeta和L-功能的根系，可以被视为一个多变量版本的维滕多zeta和L-功能。进而，对应于这些函数，得到了根系的伯努利多项式。首先，我们陈述了这些函数的几个解析性质，如解析延拓和奇点位置。其次，我们推广了Bernoulli多项式，并给出了根系zeta函数和L函数值的表达式。最后用我们以前的方法给出了它们之间的函数关系。这些关系包括扎吉尔根据维滕的工作制定的其特殊值的已知公式。
This article is essentially an announcement of the papers (7, 8, 9, 10) of the authors, though some of the examples are not included in those papers. We consider what is called zeta and L-functions of root systems which can be regarded as a multi-variable version of Witten multiple zeta and L-functions. Furthermore, corresponding to these functions, Bernoulli polynomials of root systems are dened. First we state several analytic properties, such as analytic continuation and location of singularities of these functions. Secondly we generalize the Bernoulli polynomials and give some expressions of values of zeta and L-functions of root systems in terms of these polynomials. Finally we give some functional relations among them by our previous method. These relations include the known formulas for their special values formulated by Zagier based on Witten's work.