Consequences of Universality

The phenomenon of universality has many interesting consequences. There are the classic results due to Bohr, mentioned in the introduction, as well as extensions of Ostrowski's theorem on the non-existence of algebraic di.erential equations for Dirichlet series (which actually was part of the 18th Hilbert problem). In this chapter, we prove generalizations for universal L-functions, we discuss a disproof of a conjecture on certain mean-square estimates due to Ramachandra by Andersson [1], and, finally, we study the value-distribution of linear combinations of shifts of universal Dirichlet series.