Generalizations of self-reciprocal polynomials
Abstract
A formula for the number of monic irreducible self-reciprocal polynomials, of a given degree over a finite field, was given by Carlitz in 1967. In 2011 Ahmadi showed that Carlitz's formula extends, essentially without change, to a count of irreducible polynomials arising through an arbitrary quadratic transformation. In the present paper we provide an explanation for this extension, and a simpler proof of Ahmadi's result, by a reduction to the known special case of self-reciprocal polynomials and a minor variation. We also prove further results on polynomials arising through a quadratic transformation, and through some special transformations of higher degree.
Cite
@article{arxiv.1609.07677,
title = {Generalizations of self-reciprocal polynomials},
author = {Sandro Mattarei and Marco Pizzato},
journal= {arXiv preprint arXiv:1609.07677},
year = {2023}
}
Comments
17 pages. The paper has been mildly re-organized according to suggestions of various referees, improving clarity. This version matches the published version