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.
Citation
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
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