| Abstract [eng] |
Zeta-functions are significant objects in analytic number theory. The one of the central object is the Riemann zeta -function. The well-known yet unproved Riemann hypothesis states: All non-trivial zeros of the Rieman zeta-function lies on the critical line . In analytic number theory, universality theorems have significant effect on Dirichlet L-functions and zeta-functions. Almost classical applications of universality theorems are functional independence and criteria for analogues of the Riemann hypothesis. Let s denote a complex variable and ω is a parameter from the interval (0,1]. For σ >1, the Hurwitz zeta-function is given by Denote by U a periodic sequence of complex number with the smallest period k. For σ >1 , the periodic Hurwitz zeta-function is defined by This thesis deal with the property of self-approximation related to Hurwitz and periodic Hurwitz zeta- functions. We proved that Hurwitz zeta-functions have the self-approximation property if ω is a transcendental or a rational number. Also we proved that periodic Hurwitz zeta-functions have the self-approximation property if ω is a transcendental or a rational number. |
