English

Roots of certain polynomials over finite fields

Number Theory 2023-02-28 v1

Abstract

We determine the roots in F_{q^3} of the polynomial X^{2q^k+1} + X + c for each positive integer k and each c in F_q, where q is a power of 2. We introduce a new approach for this type of question, and we obtain results which are more explicit than the previous results in this area. Our results resolve an open problem and a conjecture of Zheng, Kan, Zhang, Peng, and Li.

Keywords

Cite

@article{arxiv.2302.13478,
  title  = {Roots of certain polynomials over finite fields},
  author = {Zhiguo Ding and Michael E. Zieve},
  journal= {arXiv preprint arXiv:2302.13478},
  year   = {2023}
}

Comments

19 pages

R2 v1 2026-06-28T08:50:05.431Z