TY - JOUR
T1 - Nonsingular zeros of polynomials defined over finite fields
AU - Chakri, Lekbir
AU - Leep, David B.
N1 - Publisher Copyright:
© 2021 Taylor & Francis Group, LLC.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - Finite fields
KW - forms in many variables
KW - hypersurface
KW - nonsingular zero
KW - polynomials
UR - https://www.scopus.com/pages/publications/85113380479
UR - https://www.scopus.com/inward/citedby.url?scp=85113380479&partnerID=8YFLogxK
U2 - 10.1080/00927872.2021.1963447
DO - 10.1080/00927872.2021.1963447
M3 - Article
AN - SCOPUS:85113380479
SN - 0092-7872
VL - 50
SP - 600
EP - 614
JO - Communications in Algebra
JF - Communications in Algebra
IS - 2
ER -