PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Elementary methods for incidence problems in finite fields

Volume 177 / 2017

Javier Cilleruelo, Alex Iosevich, Ben Lund, Oliver Roche-Newton, Misha Rudnev Acta Arithmetica 177 (2017), 133-142 MSC: Primary 52C10. DOI: 10.4064/aa8225-10-2016 Published online: 22 December 2016


We use elementary methods to prove an incidence theorem for points and spheres in $\mathbb F_q^n$. As an application, we show that any point set $P\subset \mathbb F_q^2$ with $|P|\geq 5q$ 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.


  • Javier CillerueloInstituto de Ciencias Matemáticas
    Departamento de Matemáticas
    Universidad Autónoma de Madrid
    28049 Madrid, Spain
  • Alex IosevichDepartment of Mathematics
    University of Rochester
    Rochester, NY 14627, U.S.A.
  • Ben LundDepartment of Computer Science
    Rutgers, The State University of New Jersey
    Piscataway, NJ 08854, USA
  • Oliver Roche-NewtonInstitute for Financial Mathematics
    and Applied Number Theory
    Johannes Kepler Universität
    4040 Linz, Austria
  • Misha RudnevSchool of Mathematics
    University of Bristol
    University Walk
    Bristol, UK, BS8 1TW

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image