The universality theorem for Hecke L-functions

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 ζ _K (s) in the case of ${K/mathbb{Q}}$ finite abelian.