Geodesic
Analytic Properties of the Apostol-Vu Multiple Fibonacci Zeta Functions
Discussiones Mathematicae. General Algebra and Applications, Tome 40 (2020) no. 1, pp. 37-48

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In this note we study the analytic continuation of the Apostol-Vu multiple Fibonacci zeta functions ζ_AV F,k(s_1, …, s_k,; s_k+1) = ∑_1≤ m_1 lt; … lt; m_k 1/ F_m_1^s_1F_m_2^s_2⋯ F_m_k^s_kF_m_1+m_2+…+m_k^s_k+1,where s_1, ... , s_k+1 are complex variables and F_n is the n-th Fibonacci number. We find a complete list of poles and their corresponding residues.
Keywords: analytic continuation, Fibonacci numbers, multiple Fibonacci zeta function, Apostol-Vu multiple Fibonacci zeta function 
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Dutta, Utkal Keshari; Ray, Prasanta Kumar. Analytic Properties of the Apostol-Vu Multiple Fibonacci Zeta Functions. Discussiones Mathematicae. General Algebra and Applications, Tome 40 (2020) no. 1, pp. 37-48. http://geodesic.mathdoc.fr/item/DMGAA_2020_40_1_a3/