On the Value Distribution of Shifts of Universal Dirichlet Series

Shifts of universal Dirichlet series are jointly universal, that means, roughly speaking, they approximate simultaneously any given family of non-vanishing analytic functions. In this note we study consequences of this remarkable property on the value-distribution. Partially supported by the Foundation for Polish Science (FNP) and KBN grant 1 PO3A 00826. Partially supported by Lithuanian Foundation for Studies and Science.