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.
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