On Value Distribution of Certain Beurling Zeta-Functions

In this paper, the approximation of analytic functions by shifts zeta(P)(s+i tau) of Beurling zeta-functions zeta(P)(s) of certain systems P of generalized prime numbers is discussed. It is required that the system of generalized integers N-P generated by P satisfies Sigma (m <= x,m is an element of N)1=ax+O(x(delta)), a>0, 0 <=delta<1, and the function zeta(P)(s) in some strip lying in sigma<^><sigma<1, sigma<^>>delta, which has a bounded mean square. Proofs are based on the convergence of probability measures in some spaces.