3 papers
math.NT2026
Proof of a Conjecture on Primitive Quartic Polynomials over Finite Fields
Rod Gow, Gary McGuire
We present a proof of a conjecture we made about primitive polynomials, for sufficiently large. The argument follows a standard route, however a deeper result than usual with a…
math.AG2026
On the existence of a morphism between certain Artin-Schreier curves
Beatriz Barbero Lucas, Stefano Lia, Gary McGuire
It is well known that, given two curves and , defined over $\F_p$, if divides then there exists a nonconstant morphism $\m…
math.NT2024
Linearization of polynomials in prime characteristic, with applications to the Golay code and Steiner system
Rod Gow, Gary McGuire
Let be any field containing the finite field of order . A -polynomial over is an element of the polynomial ring with the property that all powers of th…