Analytic continuation of the multiple Lucas zeta functions

Abstract

This is a continuation of our previous paper [7], in which multiple Fibonacci zeta functions of depth 2 have been studied. In this article, we consider more general situation. In particular, we prove the meromorphic continuation of the multiple Lucas zeta functions of depth d:∑0<n1<⋯<nd1Un1s1⋯Undsd, where Un is the n-th Lucas number of first kind and ∑i=jdRe(si)>0 for 1≤j≤d. We compute a complete list of poles and their residues. We also prove that the multiple Lucas zeta values at negative integer arguments are rational.