The universality of zeta-functions with multiplicative coefficients

In the paper the function Z(s) = Sigma(m=1)(infinity) g(m)m-s, Rs >1 , where g(m) is a multiplicative function from the class {\cal M-beta,M-theta(c(1), c(2)) is considered. It is proved that the function Z(s) is universal, i.e. any function continuous and non-vanishing on a compact subset K of the strip {s is an element of C : beta < Rs < 1} with connected complement and analytic in the interior of K can be uniformly on K approximated by translations of the function Z(s) .