On distinct cross-ratios in positive characteristic

preprint2016arXivOpen access

Abstract

We prove that a finite subset AA of the projective line FP1FP^1 over a field FF of positive characteristic pp determines Ω(∣A∣2)Ω(|A|^2) distinct cross-ratios, as long as ∣A∣<p.|A|<\sqrt{p}.

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