PIMS Distinguished Lecture: Olivier Ramaré

Dirichlet polynomials do not take large values at close-by points. The theory of large values of Dirichlet polynomials introduced by Montgomery in 1969 elaborates on this idea. We will present the large sieve argument of Montgomery, the dissection and reflexion arguments of Huxley and the powering method of Jutila. We will end this talk by showing how such information can be used to produce density estimates for the Riemann zeta funciton.