The universality theorem for Hecke \(L\)-functions (Q444210)

The universality theorem for Hecke \(L\)-functions attached to ray class characters for functions on a disk within the strip \(\max \{\frac12,1-\frac1d\} <\text{Re}\,s<1\), \(d=[K:\mathbb Q]\), was proved by \textit{H. Mishou} [Acta Arith. 98, No. 4, 395--410 (2001; Zbl 0982.11050)]. Under the assumption of a weak version of the density hypothesis, the author extends the above result to the case of the maximal strip \( \frac12 <\text{Re}\,s<1\). As a corollary, the author gives a new proof of the universality theorem for the Dedekind zeta function in the case of finite abelian \(K/\mathbb Q\).