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arXiv · 2605.19013

Short Salem polynomials

James McKee·Chris Smyth
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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.

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James McKee, Chris Smyth. 2026-05-18. Short Salem polynomials. https://arxiv.org/abs/2605.19013

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