Revista Matemática Iberoamericana


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Volume 34, Issue 3, 2018, pp. 1093–1101
DOI: 10.4171/RMI/1017

Published online: 2018-08-27

Multiplicative energy of polynomial images of intervals modulo $q$

Kyle Castro[1] and Mei-Chu Chang[2]

(1) University of California, Riverside, USA
(2) University of California, Riverside, USA

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

Keywords: Character sums, polynomial images, subgroups of finite fields

Castro Kyle, Chang Mei-Chu: Multiplicative energy of polynomial images of intervals modulo $q$. Rev. Mat. Iberoamericana 34 (2018), 1093-1101. doi: 10.4171/RMI/1017