| Abstract [eng] |
In this paper, a theorem is obtained on the approximation in short intervals of a collection of analytic functions by shifts (z(s + ita k1), . . . , z(s + ita kr )) of the Riemann zeta function. Here, ftk :k 2 Ng is the sequence of Gram numbers, and a1, . . . , ar are different positive numbers not exceeding 1. It is proved that the above set of shifts in the interval [N, N + M], here M = o(N) as N ! ¥, has a positive lower density. For the proof, a joint limit theorem in short intervals for weakly convergent probability measures is applied. |
