Lower bound for the PerronFrobenius degrees of Perron numbers
Abstract
Using an idea of Doug Lind, we give a lower bound for the PerronFrobenius degree of a Perron number that is not totallyreal. As an application, we prove that there are cubic Perron numbers whose PerronFrobenius degrees are arbitrary large; a result known to Lind, McMullen and Thurston. A similar result is proved for biPerron numbers.
 Publication:

arXiv eprints
 Pub Date:
 November 2017
 DOI:
 10.48550/arXiv.1711.06885
 arXiv:
 arXiv:1711.06885
 Bibcode:
 2017arXiv171106885Y
 Keywords:

 Mathematics  Geometric Topology
 EPrint:
 To appear in Ergodic Theory and Dynamical Systems, 15 pages, 4 figures