Short Salem polynomials

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.

21 pages, 4 tables