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On the arithmetic and the geometry of skew-reciprocal polynomials


Author: Livio Liechti
Journal: Proc. Amer. Math. Soc. 147 (2019), 5131-5139
MSC (2010): Primary 11C08, 57M20; Secondary 11R06
DOI: https://doi.org/10.1090/proc/14668
Published electronically: July 1, 2019
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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 understanding that the difference between orientation-preserving and orientation-reversing mapping classes is at least as complicated as answering these questions.


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Additional Information

Livio Liechti
Affiliation: Department of Mathematics, University of Fribourg, Ch. du Musée 23, 1700 Fribourg, Switzerland
Email: livio.liechti@unifr.ch

DOI: https://doi.org/10.1090/proc/14668
Received by editor(s): January 7, 2019
Received by editor(s) in revised form: March 29, 2019
Published electronically: July 1, 2019
Additional Notes: The author was supported by the Swiss National Science Foundation (grant nr. 175260).
Communicated by: Ken Bromberg
Article copyright: © Copyright 2019 American Mathematical Society