Athanasios Sourmelidis: Discrete Omega results for the Riemann zeta function

Abstract:

In joint work with Paolo Minelli, we study lower bounds of the Riemann zeta function \(\zeta(s)\) along vertical arithmetic progressions on the right-half of the critical strip. We show that such bounds coincide, up to the constants in the exponential, with the ones known for the continuous case, that is when the imaginary part of s ranges on a given interval. Our methods are based on a discretization of the resonance method for estimating extremal values of the zeta function.