The Generalized Riemann Hypothesis and the discriminant of number fields

Under the Generalized Riemann Hypothesis for the Dedekind zeta-function ${\zeta }_{\kappa }$, we obtain a formula for the discriminant $D_{\kappa /\mathbb{Q}}$ of the algebraic number field κ in terms of an integral of ${\zeta }_{\kappa }$ on the critical line.