Lower bound for the Perron–Frobenius degrees of Perron numbers

Lower bound for the Perron–Frobenius degrees of Perron numbers

Using an idea of Doug Lind, we give a lower bound for the Perron–Frobenius degree of a Perron number that is not totally real, in terms of the layout of its Galois conjugates in the complex plane. As an application, we prove that there are cubic Perron numbers whose Perron–Frobenius degrees are arbi...

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Veröffentlicht in:Ergodic theory and dynamical systems 2021-04, Vol.41 (4), p.1264-1280
1. Verfasser: YAZDI, MEHDI
Format: Artikel
Sprache:eng
Schlagworte:
Lower bounds
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Beschreibung
Zusammenfassung:Using an idea of Doug Lind, we give a lower bound for the Perron–Frobenius degree of a Perron number that is not totally real, in terms of the layout of its Galois conjugates in the complex plane. As an application, we prove that there are cubic Perron numbers whose Perron–Frobenius degrees are arbitrary large, a result known to Lind, McMullen and Thurston. A similar result is proved for bi-Perron numbers.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2019.113