Number Theory Seminar

Speaker: Ikuya Kaneko

Title: Bounds for Averages of Shifted Convolution Sums

Abstract: I will discuss averages of shifted convolution sums associated to Hecke–Maaß cusp forms for GL(3) via the circle method,
Voronoï and Poisson summation, and a finite field analogue of van der Corput differencing for exponential sums. Immediate consequences of the main result include nontrivial bounds for the second moment of GL(3) L-functions in the t-aspect and the q-aspect as well as bootstrapped subconvex bounds for self-dual GL(3) × GL(2) L-functions in the spectral aspect. If time permits, I will also highlight some arithmetic implications for zero density estimates and the Rankin–Selberg problem. This is joint work with Maksym Radziwiłł at the University of Texas at Austin.