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Philadelphia Area Number Theory Seminar

Wednesday, September 18, 2019 - 2:15pm

Daniel White

Bryn Mawr College


Bryn Mawr College

Park Science Building, Room 328

Talk is scheduled to begin at 2:40 PM. Tea and refreshments will be served at 2:20 PM in the Math Lounge, Park Science Building, Room 361.

Power moments for the Riemann zeta function have enjoyed deep study over the past century. Dirichlet L-functions have natural analogues in the q-aspect, where jL(1=2; _)j2k is averaged over primitive characters _ modulo q. Power saving asymptotics are known unconditionally only up to the k = 2 case due to recent work by Young. This year, Nunes published work on a strong bound on the twelfth moment of Dirichlet L-functions to smooth squarefree moduli, an adaptation of the analogous result of Heath-Brown for the Riemann zeta function in the t-aspect. We will discuss how the framework of this proof can be applied to Dirichlet L-functions to prime power moduli and explore the rather different methods of evaluating and estimating exponential sums that arise in this setting. The content of this presentation is from recently submitted work with Djordje Milićević.