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arXiv · 1812.04918

On the arithmetic and the geometry of skew-reciprocal polynomials

Livio Liechti
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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.

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Livio Liechti. 2018-12-12. On the arithmetic and the geometry of skew-reciprocal polynomials. https://doi.org/10.1090/proc%2F14668

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