Short Salem polynomials
Number Theory
2026-05-20 v1
Abstract
We give a complete classification of all Salem polynomials of length 5. For length 6 we show that all but finitely many Salem polynomials lie in one of 12 infinite families, and subject to Lehmer's Conjecture we give a complete list of the 126 exceptions. We provide a table of short polynomials for all known Salem numbers below the smallest Pisot number.
Cite
@article{arxiv.2605.19013,
title = {Short Salem polynomials},
author = {James McKee and Chris Smyth},
journal= {arXiv preprint arXiv:2605.19013},
year = {2026}
}
Comments
21 pages, 4 tables