Multiple zeta functions at regular integer points

被引：0

作者：

Shinohara, Takeshi ^{[1
]}

机构：

[1] Nagoya Univ, Grad Sch Math, Nagoya 4648602, Japan

来源：

ACTA ARITHMETICA | 2024年 / 212卷 / 04期

关键词：

multiple zeta function; quasi-shuffle product (harmonic product); Hopf algebra; ANALYTIC CONTINUATION; VALUES; RENORMALIZATION;

D O I：

10.4064/aa221130-22-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show recurrence relations for Euler-Zagier multiple zeta functions which describe the r -fold function with one variable specialized to a non -positive integer as a rational linear combination of (r - 1) -fold functions, extending the previous results of Akiyama-Egami-Tanigawa and Matsumoto. As an application, we obtain an explicit method to calculate the special values of the multiple zeta function at any integer points (the arguments could be neither all -positive nor all -non -positive) as a rational linear combination of multiple zeta values.

引用

页码：295 / 324

页数：30

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