The value distribution of Artin L-series and zeros of Zeta-functions Original Research Article

We prove a so-called (joint) universality property of Artin L-functions. Our work is a generalization of a theorem of Voronin on Dirichlet L-functions (The Riemann Zeta-function, Walter de Gruyter, Berlin, 1992). So far we extend the theory of Harald Bohr, Jessen, Titchmarsh and Voronin on the value distributions of the Riemann Zeta-function and Dirichlet L-series. Our proofs are independent of Artinʹs conjecture on the holomorphy of Artin L-functions with non-trivial characters. In the applications, we prove that Zeta-functions of ideal classes of an arbitrary number field have infinitely many zeros in the strip image, provided that the class group is non-trivial. Further applications concern the functional independence of Dedekind Zeta-functions of normal extensions and of Artin L-functions.