Speaker
Winston Heap
Description
Mean values of Dirichlet polynomials play an important role in analytic number theory. When the length of the sum exceeds the length of the integral they pose a significant challenge requiring techniques from number theory and harmonic analysis. The mean values of these "long" Dirichlet polynomials appear in many important open problems in number theory. In this talk we survey some of these problems and then describe how, conditionally on the Riemann hypothesis, one can compute asymptotics for the moments of long Dirichlet polynomials over primes provided they are sufficiently weighted. We also give some applications to large deviations.
