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In the paper, we prove the discrete limit theorem in the sense of the weak convergence of probability measures in the space of analytic on DV = {s ∈ C : 1 < σ < 3/2, |t| 0 be a fixed real number such that exp {2πk/h} is an irrational number for all k∈Z\{0}. Then the probability measure μN(LE(s + imh)∈A), A ∈ B(H(DV)), converges weakly to the measure PLE as N→∞.

In the paper, we prove a limit theorem of discrete type on the weak convergence of probability measures on the complex plane for the periodic Hurwitz zeta-function.

In the paper, we prove a limit theorem of discrete type on the weak convergence of probability measures on the complex plane for the periodic Hurwitz zeta-function.

In the paper, a weighted limit theorem for weakly convergent probability measures on the complex plane for the periodic Hurwitz zeta function is obtained.

In this paper, the investigations of analytic and probabilistic number theory which were done in Šiauliai University are reviewed.

In the paper two-dimensional limit theorem for the modified Mellin transform of the Riemann zeta-function is obtained.

This paper provides a weak convergence theorem for weighted empirical processes of a stationary sequence under a new weak dependence condition introduced by P. Doukhan and S. Louhichi.

In the paper a discrete limit theorem in the sense of weak convergence on the complex plane for general Dirichlet series with improved condition is presented.