Additive double character sums over some structured sets and applications
Volume 199 / 2021
Acta Arithmetica 199 (2021), 135-143
MSC: 11T23, 11T30.
DOI: 10.4064/aa190628-19-1
Published online: 23 March 2021
Abstract
We study additive double character sums over two subsets of a finite field. We show that if there is a suitable rational self-map of small degree of a set $D$, then this set contains a large subset $U$ for which the standard bound on the absolute value of the character sum over $U$ and any subset $C$ (which satisfies some restrictions on its size $|C|$) can be improved. Examples of such suitable self-maps are inversion and squaring. Then we apply this new bound to trace products and sum-product equations and improve results of the first author and of Gyarmati and Sárközy.
