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In the paper, we consider simultaneous approximation of a pair of analytic functions by discrete shifts and of the absolutely convergent Dirichlet series connected to the periodic zeta-function with multiplicative sequence a, and the periodic Hurwitz zeta-function, respectively. We suppose that and as and the set is linearly independent over

It is known that zeta-functions ζ(s,F) of normalized Hecke-eigen cusp forms F are universal in the Voronin sense, i.e., their shifts ζ(s + iτ,F), τ ∈ R, approximate a wide class of analytic functions. In the paper, under a weak form of the Montgomery pair correlation conjecture, it is proved that the shifts ζ(s+iγkh,F), where γ1 < γ2 < ... is a sequence of imaginary parts of non-trivial zeros of the Riemann zeta function and h > 0, also approximate a wide class of analytic functions.

Let H(D) be the space of analytic functions on the strip . In this paper, it is proved that there exists a closed non-empty set such that every collection of the functions is approximated by discrete shifts , of Hurwitz zeta-functions with arbitrary parameters

The Lerch zeta function is defined by a Dirichlet series depending on two fixed parameters. In the paper, we consider the approximation of analytic functions by discrete shifts of the Lerch zeta function, and we prove that, for arbitrary parameters and a step of arithmetic progression, there is a closed non-empty subset of the space of analytic functions defined in the critical strip such that its functions can be approximated by discrete shifts of the Lerch zeta function. The set of those shifts is infinite, and it has a positive density. For the proof, the weak convergence of probability measures in the space of analytic functions is applied.

In this article, we survey the mathematics contest, which is held for first-year students of Šiauliai College. We discuss on the organize grounding of competition and its perspective, and on the benefit of students motivated for learning. Also, we analyze an example of the tasks and the most common errors made by students.

In the paper, the problem of simultaneous approximation of a pair of analytic functions by a pair of discrete shifts of the periodic and periodic Hurwitz zeta-function is considered. The above shifts are defined by using the sequence of imaginary parts of non-trivial zeros of the Riemann zeta-function. For the proof of approximation theorems, a weak form of the Montgomery pair correlation conjecture is applied.

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 joint limit theorem for weakly convergent probability measures in ℂ r for periodic Hurwitz zeta-functions with algebraic irrational parameters satisfying certain independence conditions is obtained.

In the article, main attention is given to the compatibility of study subjects of mathematics in studies programs of physical sciences “Business Informatics” and “Informatics”‘ at Šiauliai State College and Šiauliai University, respectively. Also, we review the normative documents regulating the order of study results in higher education.