2015/08/20 by Misha Rudnev, Rudnev, Misha
Arts and Humanities · Mathematics · #Algebraic Geometry and Number Theory #Finite Group Theory Research #French Historical and Cultural Studies #math.CO #msc:11B75 #msc:68R05
paper · pdf · doi:10.48550/arxiv.1508.05142
This article had been earlier withdrawn by the author: the main proposition was false as stated.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 $Ω(|A|^{3/2})$ 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
arxiv created 2016/01/08 · arxiv updated 2016/01/11
We prove that a finite subset A of the projective line FP1 over a field F of positive characteristic p determines Ω(|A|2) distinct cross-ratios, as long as |A|<√(p).