Analytic continuation of multiple Hurwitz zeta functions

We use a variant of a method of Goncharov, Kontsevich and Zhao [ 5 , 16 ] to meromorphically continue the multiple Hurwitz zeta function to Cᵈ , to locate the hyperplanes containing its possible poles and to compute the residues at the poles. We explain how to use the residues to locate trivial zeros of ζd(s;θ) .