Darius Šiaučiūnas

A mixed joint universality theorem for zeta‐functions

AbstractIn the paper, a joint universality theorem on the approximation of analytic functions for zeta-function of a normalized Hecke eigen cusp form and a collection of periodic Hurwitz zeta-functions with algebraically independent parameters is obtained.

On zeta-functions associated to certain cusp forms. II

A formula for the mean value of multiplicative functions associated to certain cusp forms is obtained. The paper is a continuation of [4].

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.

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.

On the Modulus of the Selberg Zeta-Functions in the Critical Strip

We investigate the behavior of the real part of the logarithmic derivatives of the Selberg zeta-functions ZPSL(2,Z)(s) and ZC (s) in the critical strip 0 < σ < 1. The functions ZPSL(2,Z)(s) and ZC (s) are defined on the modular group and on the compact Riemann surface, respectively.

Mellin Transform of Dirichlet L-Functions with Primitive Character

AbstractIn the paper, meromorphic continuation for the modified Mellin transform of Dirichlet L-functions with primitive character is obtained.