### Twisted correlations of the divisor function via discrete averages of SL(2,R) Poincaré series

Heilbronn Number Theory Seminar

6th November 2024, 4:00 pm – 5:00 pm

Fry Building, 2.04

The talk is based on joint work with Lasse Grimmelt. We prove a theorem that allows one to count solutions to determinant equations twisted by a periodic weight with a high uniformity in the modulus. It is obtained by using the spectral methods of SL(2,R) automorphic forms to study Poincaré series over congruence subgroups while keeping track of interactions between multiple orbits. The approach offers increased flexibility over the widely used sums of Kloosterman sums techniques. We give applications to correlations of the divisor function twisted by periodic functions and the fourth moment of Dirichlet L-functions on the critical line.

## Comments are closed.