| Abstract [eng] |
The approximation of analytic functions by simpler or more general functions is one of the more challenging tasks for mathematicians. This dissertation is devoted to universal functions, i.e., to functions whose shifts can approximate a wide class of analytic functions. The object of the dissertation is zeta-functions associated with normalized simultaneous Hecke-eigen cusp forms (or zeta-functions of cusp forms). In 2001, A. Laurinčikas and K. Matsumoto proved that zeta-functions of cusp forms are universal in the Voronin sense, i.e., that any non-vanishing holomorphic function can be approximated uniformly with a given accuracy by a certain shift of a zeta function of cusp forms. In this dissertation, three generalizations of the Laurinčikas-Matsumoto theorem are proved, namely, continuous, discrete and joint discrete cases. In these theorems, non-linear shifts are taken using a special class of functions with some natural growth conditions. Moreover, modified universality theorems are proved when the lower limit is replaced by the limit. |
