Improved lower bounds for the discriminants of number fields

We improve the currently known lower bounds for the discriminant of a number field without assuming the generalized Riemann hypothesis. Our method does not perform computer searches. Instead, it exploits the hypothetical presence of zeros of the Dedekind zeta function of a number field off the critical line. Although we present our results for number fields of degrees 9 and 10, the method can be applied to any signature.