| Abstract [eng] |
Let q(t) denote the increment of the argument of the product p−s/2G(s/2) along the segment connecting the points s = 1/2 and s = 1/2 + it, and tn denote the solution of the equation q(t) = (n − 1)p, n = 0, 1, . . . . The numbers tn are called the Gram points. In this paper, we consider the approximation of a collection of analytic functions by shifts in the Riemann zeta-function (z(s + ita k1), . . . , z(s + ita kr )), k = 0, 1, . . . , where a1, . . . , ar are different positive numbers not exceeding 1. We prove that the set of such shifts approximating a given collection of analytic functions has a positive lower density. For the proof, a discrete limit theorem on weak convergence of probability measures in the space of analytic functions is app. |
