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

Driss Essouabri; Kohji Matsumoto; Hirofumi Tsumura

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

机译：与线性递归序列和矢量和公式关联的多个Zeta函数

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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 sum formula can be deduced.

机译：我们证明了某些多元变量zeta函数的全纯连续性，其系数满足适当的递归条件。实际上，我们介绍了更多一般的矢量zeta函数，并证明了它们的全纯连续性。此外，我们在矢量zeta函数中展示了一个矢量和公式，从中可以得出经典和公式的一些概括。

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来源
《Canadian Journal of Mathematics》 |2011年第2期|共36页
作者
Driss Essouabri; Kohji Matsumoto; Hirofumi Tsumura;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Zeta-functions; holomorphic continuation; recurrence sequences; Fibonacci numbers; sum formulas;

机译：Zeta函数;全同连续;递归序列;斐波那契数;求和公式;

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1. Multiple Zeta-Functions Associated with Linear Recurrence Sequences and the Vectorial Sum Formula [J] . Driss Essouabri, Kohji Matsumoto, Hirofumi Tsumura Canadian Journal of Mathematics . 2011,第2期

机译：与线性递归序列和矢量和公式关联的多个Zeta函数
2. A Four-Order Linear Recurrence Formula Involving the Quartic Gauss Sums and One Kind Two-Term Exponential Sums [J] . Lan Qi, Xingxing Lv Journal of Mathematics . 2021,第a期

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3. On Vectorized Weighted Sum Formulas of Multiple Zeta Values [J] . Chung Chan-Liang, Ong Yao Lin Taiwanese journal of mathematics . 2016,第2期

机译：多个Zeta值的矢量化加权和公式
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7. A Study On Sum Formulas of Generalized Sixth-Order Linear Recurrence Sequences [O] . Yüksel Soykan 2020

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

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