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

Prahlad Sharma

paper

Bilinear sums with $G L (2)$ coefficients and the exponent of distribution of $d_{3}$

arXiv:2303.06087

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 $G L (2)$ coefficients obtained using the delta symbol approach.

Final version. To appear in Proc. London Math. Soc

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

Abstract

Bilinear sums with $G L (2)$ coefficients and the exponent of distribution of $d_{3}$