A note on hyperquadratic elements of low algebraic degree
Number Theory
2019-10-08 v1
Abstract
In different areas of discrete mathematics, a certain type of polynomials, having coefficients in a field K of finite characteristic, has been considered. The form and the degree of these polynomials, here called projective, are simply linked to the characteristic p of K. Roots of these projective polynomials are particular algebraic elements over K, called hyperquadratic. For a general algebraic element of degree d over K, we discuss the possibility of being hyperquadratic. Using a method of differential algebra, we obtain, for particular fields K = Fp, projective polynomials only having polynomial factors of degree 1 or 2.
Cite
@article{arxiv.1910.02648,
title = {A note on hyperquadratic elements of low algebraic degree},
author = {Alain Lasjaunias},
journal= {arXiv preprint arXiv:1910.02648},
year = {2019}
}