Elementary methods for incidence problems in finite fields

Cilleruelo Javier, Alex Iosevich, Ben Lund, Oliver Roche-Newton, Misha Rudnev

Research output: Contribution to journalArticle (Academic Journal)peer-review

2 Citations (Scopus)
278 Downloads (Pure)

Abstract

We use elementary methods to prove an incidence theorem for points and spheres in Fnq. As an application, we show that any point set P⊂F2q 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.
Original languageEnglish
Pages (from-to)133-142
Number of pages10
JournalActa Arithmetica
Volume177
Early online date22 Dec 2016
DOIs
Publication statusPublished - 2017

Keywords

  • incidences
  • circles
  • finite fields

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