Prahlad Sharma: Bilinear sums with (GL(2)) coefficients and the exponent of distribution of (d_3)

Speaker
Prahlad Sharma, MPI Bonn

Abstract
We obtain the exponent of distribution $1/2+1/30$ for the ternary divisor function $d_3$ to square-free and prime power moduli, improving the previous results of Fouvry–Kowalski–Michel, Heath-Brown, and Friedlander–Iwaniec. The key input is certain estimates on bilinear sums with $GL(2)$ coefficients obtained using the delta symbol approach.