Workshop: A lower bound on high moments of character sums , Barnabás Szabó

Speaker
Barnabás Szabó, University of Warwick

Abstract
Let \(k\geq 2\) be a real number. We prove a lower bound on the \(2k\)-th moment of unweighted Dirichlet character sums which is conjecturally sharp up to a constant. During the process, we explore the deep connection between Dirichlet characters and the Steinhaus random multiplicative function. We also discuss some related results, in particular the corresponding upper bound which is known to hold under Generalised Riemann Hypothesis.