On the Hurwitz Zeta-Function with Algebraic Irrational Parameter. II

It is known that the Hurwitz zeta-function with transcendental or rational parameter has a discrete universality property; i.e., the shifts , , , approximate a wide class of analytic functions. The case of algebraic irrational is a complicated open problem. In the paper, some progress in this problem is achieved. It is proved that there exists a nonempty closed set of analytic functions such that the functions in are approximated by the above shifts. Also, the case of certain compositions is discussed.