Alexandre de Faveri

The sixth moment of the Riemann zeta function

We prove new large value estimates for the Riemann zeta function on the critical line. For instance, we improve the upper bound on the measure of $t\in [T, 2T]$ with $|\zeta(1/2 + it)| \geq T^{1/8}$ for the first time since Hardy-Littlewood (1923). Our results imply improved upper bounds on the $k$-th moment of zeta fo...