Renata Macaitienė

The discrete universality of the periodic Hurwitz zeta function

The periodic Hurwitz zeta function , s=σ+it, 01, by and by analytic continuation elsewhere. Here {a m } is a periodic sequence of complex numbers. In this paper, a discrete universality theorem for the function with a transcendental parameter α is proved. Roughly speaking, this means that every analytic function can be approximated uniformly on compact sets by shifts , where m is a non-negative integer and h is a fixed positive number such that is rational.

Discrete universality theorems for the Hurwitz zeta-function

In the paper, we obtain a discrete universality theorem on approximation of analytic functions by discrete shifts of the Hurwitz zeta-function under a new hypothesis on the parameter generalizing the transcendence condition.

Joint Universality of Dirichlet L-Functions and Periodic Hurwitz Zeta-Functions

Abstract In the paper, we prove that every system of analytic functions can be approximated simultaneously uniformly on compact subsets of some region by a collection consisting of shifts of Dirichlet L-functions with pairwise non-equivalent characters and periodic Hurwitz zeta-functions with parameters algebraically independent over the field of rational numbers.

A Weighted Universality Theorem for Periodic Zeta-Functions

AbstractThe periodic zeta-function ζ(s; a), s = σ + it is defined for σ > 1 by the Dirichlet series with periodic coefficients and is meromorphically continued to the whole complex plane. It is known that the function ζ(s; a), for some sequences a of coefficients, is universal in the sense that its shifts ζ(s + iτ ; a), τ ∈ ℝ, approximate a wide class of analytic functions. In the paper, a weighted universality theorem for the function ζ(s; a) is obtained.

The characteristic transforms on ℝ×ℂ

A multiplicative version of characteristic transforms for probability measures on ℝ×ℂ is defined, and continuity theorems in terms of these transforms are proved.

A WEIGHTED DISCRETE UNIVERSALITY THEOREM FOR PERIODIC ZETA-FUNCTIONS. II

AbstractIn the paper, a weighted theorem on the approximation of a wide class of analytic functions by shifts ζ(s + ikαh; 𝔞), k ∈ ℕ, 0 0, of the periodic zeta-function ζ(s; 𝔞) with multiplicative periodic sequence 𝔞, is obtained.

Universality Theorems for Some Composite Functions

In [5], it was proved that a collection consisting from Dirichlet L-functions and periodic Hurwitz zeta-functions is universal in the sense that the shifts of those functions approximate simultaneously a given collection of analytic functions. In the paper, we prove theorems on the universality of composite functions of the above collection.

The joint universality of Dirichlet L -functions and Lerch zeta-functions

We establish a Voronin-type joint universality theorem on approximating analytic functions by the translations of Dirichlet L-functions and Lerch zeta-functions.