Multiplicative energy of polynomial images of intervals modulo \(q\). (English) Zbl 1454.11153
Summary: Given a smooth integer \(q\), we use existing upper bounds for character sums to find a lower bound for the size of a multiplicative subgroup of the integers modulo \(q\) which contains the image of an interval of consecutive integers \(I\subset\mathbb{Z}_q\) under a polynomial \(f\in\mathbb{Z}[X]\).