Paper of Lincoln algebraist accepted in a high-ranking journal

A paper by Sandro Mattarei and Marco Pizzato, Irreducible polynomials from a cubic transformation, has been accepted for publication in the journal Finite Fields and Their Applications. (See https://arxiv.org/abs/2111.04166 for a preprint version, or wait a short time for the published version, which will be open access.) Marco was Sandro’s PhD student at the University of Trento, and the paper contains further developments of some of the work in Marco’s PhD thesis of 2013.

Abstract: Let $R(x)=g(x)/h(x)$ be a rational expression of degree three over the finite field $\mathbb{F}_q$ . We count the irreducible polynomials in $\mathbb{F}_q[x]$ , of a given degree, which have the form $h(x)^{\deg f}\cdot f\bigl(R(x)\bigr)$ for some $f(x)\in\mathbb{F}_q[x]$ . As an example of application of our results, we recover the number of irreducible transformation shift registers of order three, which were computed by Jiang and Yang in 2017.