JOINT VALUE DISTRIBUTION THEOREMS FOR THE RIEMANN AND HURWITZ ZETA-FUNCTIONS

In the paper, a class of functions phi(t) is introduced such that a given pair of analytic functions is approximated simultaneously by shifts zeta (s + i phi(k)), zeta (s + i phi(k), alpha), k is an element of N, of the Riemann and Hurwitz zeta-functions with parameter a for which the set {(logp: p is prime), (log(m + alpha): m is an element of N-0)} is linearly independent over Q. The definition of this class includes an estimate for phi(t) and phi'(t) as well as uniform distribution modulo 1 of the sequence {a phi(k): k is an element of N}, a not equal 0.