Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH

Abstract

Let \psi_\K be the Chebyshev function of a number field \K. Under GRH we prove an explicit upper bound for |\psi_\K(x)-x| in terms of the degree and the discriminant of \K. The new bound improves significantly on previous known results.Comment: Some misprints corrected. This is the final version which will appear in Mathematics of Computatio