Bilinear sums with GL(2)$GL(2)$ coefficients and the exponent of distribution of d3$d_3$

Abstract

AbstractWe obtain the exponent of distribution for the ternary divisor function 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 coefficients obtained using the delta symbol approach.