Multiple Zeta-Functions Associated with Linear Recurrence Sequences and the Vectorial Sum Formula

被引：6

作者：

Essouabri, Driss ^{[1
]}

Matsumoto, Kohji ^{[2
]}

Tsumura, Hirofumi ^{[3
]}

机构：

[1] Univ St Etienne, PRES Univ Lyon, Fac Sci, Dept Math, F-42023 St Etienne 2, France

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

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

来源：

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2011年 / 63卷 / 02期

关键词：

Zeta-functions; holomorphic continuation; recurrence sequences; Fibonacci numbers; sum formulas; ANALYTIC CONTINUATION; NEGATIVE INTEGERS; T-TUPLES; VALUES; POLYNOMIALS; NUMBER;

D O I：

10.4153/CJM-2010-085-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the holomorphic continuation of certain multi-variable multiple zeta-functions whose coefficients satisfy a suitable recurrence condition. In fact, we introduce more general vectorial zeta-functions and prove their holomorphic continuation. Moreover, we show a vectorial sum formula among those vectorial zeta-functions from which some generalizations of the classical suns formula can be deduced.

引用

页码：241 / 276

页数：36

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