| Abstract [eng] |
In the paper, we consider the approximation of analytic functions by shifts from the wide class (S) over tilde of L-functions. This class was introduced by A. Selberg, supplemented by J. Steuding, and is defined axiomatically. We prove the so-called joint discrete universality theorem for the function L (s) is an element of(S) over tilde. Using the linear independence over Q of the multiset {(h(j) log p : p is an element of P), j = 1,..., r; 2 pi} for positive h(j), we obtain that there are many infinite shifts (L(s + ikh(1)),..., L (s + ikh(r))), k = 0, 1,..., approximating every collection (f1(s),..., fr(s)) of analytic non-vanishing functions defined in the strip {s is an element of C : sigma(L) < sigma < 1}, where sigma(L) is a degree of the function L(s). For the proof, the probabilistic approach based on weak convergence of probability measures in the space of analytic functions is applied. |
