On distinct cross-ratios in positive characteristic
Combinatorics
2016-01-11 v6
Abstract
We prove that a finite subset of the projective line over a field of positive characteristic determines distinct cross-ratios, as long as
Cite
@article{arxiv.1508.05142,
title = {On distinct cross-ratios in positive characteristic},
author = {Misha Rudnev},
journal= {arXiv preprint arXiv:1508.05142},
year = {2016}
}
Comments
This article had been earlier withdrawn by the author: the main proposition was false as stated. This update is to point out that the bound $\Omega(|A|^{3/2})$ for the number of distinct cross-ratios, and other incidence estimates have been proven in the preprint "Growth Estimates in Positive Characteristic via Collisions", with E. Aksoy, B. Murphy and I. Shkredov, arXiv:1512.06613