Math Department Colloquium Talk - Dr. Joseph Leung

Dr. Joseph Leung, Univeristy of Oklahoma https://math.ou.edu/profile?jleung

Title: Moments and shifted sums beyond GL(2)

Abstract: Moments of the Riemann zeta function play a central role in understanding the distribution of primes. Classical work of Hardy–Littlewood and Ingham established the asymptotics of the second and fourth moments nearly a century ago, yet the sixth moment remains out of reach. These moments are connected to the shifted sum problem of divisor functions, and the main obstacle is that we cannot analyze shifted sums beyond GL(2). In this talk, I will present some recent progress towards overcoming this barrier. After describing some results on the GL(3) shifted sums, I will introduce a new method to tackle shifted sums beyond GL(2). Developed with Matthew Young, this method relies on a novel reinterpretation of the Duke-Friedlander-Iwaniec delta method, and we apply it to study Sp(4) shifted sums.