With early contributions due to, among others, Besicovitch, Bohr, Bohnenblust, Hardy, Hille, Riesz, Neder and Landau, the last 20 years show a substantial revival of systematic research on ordinary Dirichlet series $\sum a_n n^{-s}$, more recently eve

In this article, we obtain the analytic continuation of multiple shifted Lucas zeta function, L-function associated with Dirichlet characters and additive characters. We then compute a list possible singularities residues these functions at poles. Further, show rationality L-functions quadratic negative integer arguments.