Matthew Young

The Weyl bound for Dirichlet L-functions

The problem of bounding L-functions has a long history. For the Riemann zeta function, the method of Weyl gives a subconvexity bound with exponent 1/6, which is now called the Weyl bound. Many questions on the zeta function in the t-aspect have a natural analog for Dirichlet L-functions in the q-aspect, but the latter is in general much harder. Indeed, the first subconvexity result for Dirichlet L-functions, due to Burgess in the 1960's, has a weaker exponent 3/16. In this talk I will discuss work with Ian Petrow that proves the Weyl bound for all Dirichlet L-functions.