Analytic continuation of the multiple Fibonacci zeta functions

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Sudhansu Sekhar Rout¹  Nabin Kumar Meher² 

[1] Institute of Mathematics and Applications;Harish-Chandra Research Institute

关键词: Analytic continuation;    multiple Fibonacci zeta function;    poles and residues.;   

DOI  :  10.3792/pjaa.94.64

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

In this article, we prove the meromorphic continuation of the multiple Fibonacci zeta functions of depth 2: \begin{equation*} \sum_{0 0$ and $\mathop{\mathrm{Re}} (s_{2}) > 0$. We compute a complete list of its poles and their residues. We also prove that multiple Fibonacci zeta values at negative integer arguments are rational.

【 授权许可】

Unknown