On the exponent of distribution of the ternary divisor function

Étienne Fouvry, Emmanuel Kowalski, Philippe Michel

Published 2013-04-11, updated 2014-01-27Version 2

We show that the exponent of distribution of the ternary divisor function $d_3$ in arithmetic progressions to prime moduli is at least 1/2+1/46, improving results of Heath-Brown and Friedlander--Iwaniec. Furthermore, when averaging over a fixed residue class, we prove that this exponent is increased to 1/2 +1/34.