On the arithmetic and the geometry of skew-reciprocal polynomials

Abstract

We reformulate Lehmer's question from 1933 and a question due to Schinzel and Zassenhaus from 1965 in terms of a comparison of the Mahler measures and the houses, respectively, of monic integer reciprocal and skew-reciprocal polynomials of the same degree. This entails that understanding the difference between orientation-preserving and orientation-reversing mapping classes is at least as complicated as answering these questions.