Points below a parabola in affine planes of prime order.

  • Published In: Bulletin of the Belgian Mathematical Society - Simon Stevin, 2025, v. 32, n. 3. P. 332 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Adriaensen, Sam; Weiner, Zsuzsa 3 of 3

Abstract

The elements of a finite field of prime order canonically correspond to the integers in an interval. This induces an ordering on the elements of the field. Using this ordering, Kiss and Somlai recently proved interesting properties of the set of points below the diagonal line. It is already surprising that a set in AG(2, p) defined in such a way can exhibit notable properties. In this paper, we present another unexpected result in a similar vein. We investigate the set of points lying below a parabola. We prove that in some sense, this set of points looks the same from all but two directions, despite having only one non-trivial automorphism. In addition, we study the sizes of these sets, and their intersection numbers with respect to lines. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Bulletin of the Belgian Mathematical Society - Simon Stevin. 2025/08, Vol. 32, Issue 3, p332
  • Document Type:Article
  • Subject Area:Mathematics
  • Publication Date:2025
  • ISSN:1370-1444
  • DOI:10.36045/j.bbms.241203
  • Accession Number:187681502
  • Copyright Statement:Copyright of Bulletin of the Belgian Mathematical Society - Simon Stevin is the property of Department of Pure Mathematics & Computer Algebra, Ghent University and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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