Elementary methods for incidence problems in finite fields

2014/07/09 by Cilleruelo, Javier, Iosevich, Alex, Lund, Ben +2 · 1 citation
#52C10 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1407.2397

Abstract

We use elementary methods to prove an incidence theorem for points and spheres in \mathbbF_qⁿ. As an application, we show that any point set of P⊂ \mathbbF_q² with |P|≥ 5q determines a positive proportion of all circles. The latter result is an analogue of Beck's Theorem for circles which is optimal up to multiplicative constants.

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• Sphere intersections and incidences over finite fields

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