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June 2018 Analytic continuation of the multiple Fibonacci zeta functions
Sudhansu Sekhar Rout, Nabin Kumar Meher
Proc. Japan Acad. Ser. A Math. Sci. 94(6): 64-69 (June 2018). DOI: 10.3792/pjaa.94.64

Abstract

In this article, we prove the meromorphic continuation of the multiple Fibonacci zeta functions of depth 2: \begin{equation*} \sum_{0<n_{1}<n_{2}}\frac{1}{F_{n_{1}}^{s_{1}}F_{n_{2}}^{s_{2}}}, \end{equation*} where $F_{n}$ is the $n$-th Fibonacci number, $\mathop{\mathrm{Re}} (s_{1}) > 0$ 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.

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Sudhansu Sekhar Rout. Nabin Kumar Meher. "Analytic continuation of the multiple Fibonacci zeta functions." Proc. Japan Acad. Ser. A Math. Sci. 94 (6) 64 - 69, June 2018. https://doi.org/10.3792/pjaa.94.64

Information

Published: June 2018
First available in Project Euclid: 31 May 2018

zbMATH: 06941824
MathSciNet: MR3808539
Digital Object Identifier: 10.3792/pjaa.94.64

Subjects:
Primary: 11M99
Secondary: 11B39 , 30D30

Keywords: analytic continuation , multiple Fibonacci zeta function , poles and residues

Rights: Copyright © 2018 The Japan Academy

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Vol.94 • No. 6 • June 2018
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