Analytic continuation of the multiple Fibonacci zeta functions

Abstract

: In this article, we prove the meromorphic continuation of the multiple Fibonacci zeta functions of depth 2: where F n is the n -th Fibonacci number, Re ð s 1 Þ > 0 and Re ð s 2 Þ > 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.