USask Mathematics & Statistics Colloquium: Habiba Kadiri

This talk will first provide a (non-exhaustive) survey of explicit results on zero-free regions and zero densities of the Riemann zeta function and their relationship to error terms in the prime number theorem. This will be extended to Dirichlet L functions and Dedekind zeta functions, where new challenges arise with potential exceptional zeros. We will explore estimates for the error terms for prime counting functions across various contexts, including number fields.