A Joint Limit Theorem for Epstein and Hurwitz Zeta-Functions

In the paper, we prove a joint limit theorem in terms of weak convergence of probability measures on C² defined by means of the Epstein ζ(s;Q) and Hurwitz ζ(s,α) zeta-functions. The limit measure in the theorem is explicitly given. For this, some restrictions on the matrix Q and parameter α are required. The theorem obtained extends and generalizes Bohr-Jessen’s results characterising asymptotic behaviour of the Riemann zeta-function.