  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.
