Let $f$ be a quadratic polynomial with leading coefficient $\alpha$, and suppose $\alpha$ is in a "minor arc" in the sense that $\alpha$ is not within $\frac{(\log N)^A}{q N^2}$ of any rational number $\frac{a}{q}$ with $q < (\log N)^A$. My advisor told me that the following holds:
$\sum_{n=1}^N \Lambda(n) e(f(n)) \lesssim N (\log N)^{-C(A)}$
Where $\Lambda$ is the Von Mangoldt function and $C$ is some unbounded increasing function in $A$. Could someone please help me find a reference for this statement?