Joint universality for $L$-functions from Selberg's class and periodic Hurwitz zeta-functions

Universality (in the Voronin sense [1]) of zeta and $L$-functions is one of the most interesting phenomenon of analytic number theory - it is known that their shifts approximate uniformly on compact subsets of certain regions wide classes of analytic functions. In the talk, we will consider so called mixed joint universality [2], i.e., we will show that every system of analytic functions can be approximated simultaneously uniformly on compact subsets of some region by a collection consisting of shifts of $L$-functions from the Selberg class and periodic Hurwitz zeta-functions.
[1] S. M. Voronin. Theorem on the “universality” of the Riemann zeta-function. Izv. Akad. Nauk. SSSR, Ser. Matem., 39 (1975), № 3, 475–486, 1975 (in Russian).
[2] H. Mishou, The joint value-distribution of the Riemann zeta function and Hurwitz zeta functions. — Lith. Math. J., 47(2007), № 1, 32-47.