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
JournalCommunications in Algebra
StateAccepted/In press - 2021

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