On discrete universality of composite functions
In 1975, S.M. Voronin proved that the Riemann zeta-function ζ (s) is universal in the sense that its shifts approximate uniformly on some sets any analytic function. Let h be a fixed positive number such that exp is irrational for all . In the paper, the classes of functions F such that the shifts F (ζ (s + imh)), , approximate any analytic function are presented. For the proof of theorems, some elements of the space of analytic functions are applied.
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