Equidistribution of a quadratic polynomial with irrational leading coefficient

If $a$ is irrational and $b,c$ are real, the fractional parts of $a{n}^2+bn+c$ form an equidistributed sequence. In the Van der Corput lemma, every nonzero-lag correlation of $e^{2\pi im(a{n}^2+bn+c)}$ is a geometric series with irrational frequency $2mah$ and tends to zero. The Weyl criterion then applies.