The universality theorem for Hecke L-functions

Abstract

We extend the universality theorem for Hecke L-functions attached to ray class characters from the previously known strip \({ \max \{\frac{1}{2}, 1-\frac{1}{d}\} < {\rm Re}\,s < 1}\) for \({d=\left[K:\mathbb{Q}\right]}\) to the maximal strip \({\frac{1}{2} < {\rm Re}\,s < 1}\) under an assumption of a weak version of the density hypothesis. As a corollary, we give a new proof of the universality theorem for the Dedekind zeta function ζK(s) in the case of \({K/\mathbb{Q}}\) finite abelian.