| Abstract [eng] |
The Lerch zeta-function defined, for sigma greater than 1, by the Dirichlet series and by analytic continuation elsewhere, is investigated. The main attention is devoted to the universality of the Lerch zeta-function i.e., to approximation of analytic functions by shifts. Continuous an discrete universality theorems for the Lerch zeta-function are obtained. These theorems extend the known results for the Lerch zeta-function. The used conditions for the parameter alpha are expressed by the linear independence over the field of rational numbers of some sets. Also, joint universality theorems for a collection of Lerch zeta-functions are obtained. In this case, a given collection of analytic functions are simultaneously approximated by shifts. Universality of the Lerch zeta-function is applied to prove its functional independence. The results of the thesis cover all known universality results for the Lerch zeta-function. |
