The distribution of the Riemann zeta-function at its relative maxima

On the critical line, the modulus of Riemann zeta-function has exactly one relative maximum between consecutive zeros assuming the Riemann hypothesis. In this talk I will discuss the distribution of values of the Riemann zeta-function at these relative maxima and give an application to counting the number of solutions $T \le t \le 2T$ to the equation $|\zeta(\tfrac12+it)|=a$, where $a>0$ is a real number. This is joint work with Micah Milinovich.