Exponential sums with reducible polynomials

Cécile Dartyge, Greg Martin

Hooley proved that if $f\in \mathbb{Z}[X]$ is irreducible of degree $\ge 2$, then the fractions $\{r/n\}$, $0<r<n$ with $f(r)\equiv 0(\mathrm{mod}n)$, are uniformly distributed in $(0,1)$. I…