# Multiplicative energy of polynomial images of intervals modulo $q$

### Kyle Castro

University of California, Riverside, USA### Mei-Chu Chang

University of California, Riverside, USA

## Abstract

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 $f \in \mathbb{Z}[X]$.

## Cite this article

Kyle Castro, Mei-Chu Chang, Multiplicative energy of polynomial images of intervals modulo $q$. Rev. Mat. Iberoam. 34 (2018), no. 3, pp. 1093–1101

DOI 10.4171/RMI/1017