Product of Sets on Varieties in Finite Fields
Journal
Journal of Fourier Analysis and Applications
Journal Volume
30
Journal Issue
2
ISSN
1069-5869
1531-5851
Date Issued
2024-03-27
Author(s)
Abstract
Let V be a variety in Fqd and E⊂V. It is known that if any line passing through the origin contains a bounded number of points from E, then ∏(E)=|{x·y:x,y∈E}|≫q whenever |E|≫qd2. In this paper, we show that the barrier d2 can be broken when V is a paraboloid in some specific dimensions. The main novelty in our approach is to link this question to the distance problem in one lower dimensional vector space, allowing us to use recent developments in this area to obtain improvements.
Publisher
Springer Science and Business Media LLC
Type
journal article