On a paucity result in Incidence Geometry

Name: On a paucity result in Incidence Geometry
Creator: Shkredov, Ilya D.
Keywords: Mathematics - Number Theory, FOS: Mathematics, Mathematics - Combinatorics, 0102 computer and information sciences, Number Theory (math.NT), Combinatorics (math.CO), 0101 mathematics, 01 natural sciences

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2022Embargo end date: 01 Jan 2022Publisher:arXiv

Authors: Shkredov, Ilya D.;

doi: 10.48550/arxiv.2201.08037

arXiv: http://arxiv.org/abs/2201.08037

On a paucity result in Incidence Geometry

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Abstract

We obtain some asymptotic formulae (with power savings in their error terms) for the number of quadruples in the Cartesian product of an arbitrary set $A \subset \mathbf{R}$ and for the number of quintuplets in $A\times A$ for any subset $A$ of the prime field $\mathbf{F}_p$. Also, we obtain some applications of our results to incidence problems in $\mathbf{F}_p$.

14 pages

Keywords

Mathematics - Number Theory, FOS: Mathematics, Mathematics - Combinatorics, Number Theory (math.NT), Combinatorics (math.CO)

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