Nonsingular zeros of polynomials defined over finite fields

Lekbir Chakri, David B. Leep

Research output: Contribution to journalArticlepeer-review


The aim of this paper is to study the existence of nontrivial, nonsingular zeros of a nonhomogeneous polynomial defined over a finite field. To accomplish this, we determine conditions that guarantee the existence of a prescribed number of nonsingular zeros of a homogeneous form f over a finite field k that are not zeros of a homogeneous form h when f, h are relatively prime. The cases of quadratic and cubic polynomials are considered in detail. This extends previous results that have usually considered only the homogeneous case.

Original languageEnglish
Pages (from-to)600-614
Number of pages15
JournalCommunications in Algebra
Issue number2
StatePublished - 2022

Bibliographical note

Publisher Copyright:
© 2021 Taylor & Francis Group, LLC.


  • Finite fields
  • forms in many variables
  • hypersurface
  • nonsingular zero
  • polynomials

ASJC Scopus subject areas

  • Algebra and Number Theory


Dive into the research topics of 'Nonsingular zeros of polynomials defined over finite fields'. Together they form a unique fingerprint.

Cite this