An estimate of the order of the Hecke-Landau \(\zeta\) (s,\(\chi\) )- functions (Q1823991)

With \(\zeta\) (s,\(\chi)\) denoting the Hecke-Landau zeta-functions over an algebraic number field K of degree \( n,\) the author obtains an explicit estimate for \(| (s-1)\zeta (s,\chi)|\) in the region \(0\leq \sigma \leq 1\), \(-\infty <t<\infty\). The estimate is given in terms of the discriminant of K, and the norm of the conductor of \(\chi\). Similar results were obtained for the Dedekind zeta-functions \(\zeta_ K(s)\) by \textit{J. K. Wieczorkiewicz} [Funct. Approx., Comment. Math. 7, 9- 12 (1979; Zbl 0408.12014)].