| Abstract [eng] |
In the thesis, the problems related to the discrete universality of the Riemann and Hurwitz zeta-functions and , , , which are defined, for , by the series and and by analytic continuation elsewhere, are considered. Let be the space of analytic functions on equipped with the topology of uniform convergence on compacta, be the class of compact subsets of the strip with connected complements, and let , , be the class of continuous functions on which are analytic in the interior of . In Chapter 1, universality theorems on the uniform approximation on compact sets of functions by shifts , where are certain continuous operators, is a fixed number, and runs non-negative integers, are obtained. Chapter 2 is devoted to the discrete universality of composite functions $ for some classes of operators and transcendental or rational parameters . Here analogues of theorems of Chapter 1 are proved for the Hurwitz zeta-function. Chapter 3 contains the results of applications of discrete universality theorems from Chapters 1 and 2 to zero distribution of composite functions and . In Chapter 4, a discrete universality theorem for $ with from a new class is obtained. This class is characterized by the linear independence over the field of rational numbers of the set for all positive rational nd generalizes the case of transcendental parameters . |
