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 |
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| container_title | Ergodic theory and dynamical systems |
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| creator | YAZDI, MEHDI |
| description | 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. |
| doi_str_mv | 10.1017/etds.2019.113 |
| format | Article |
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| ispartof | Ergodic theory and dynamical systems, 2021-04, Vol.41 (4), p.1264-1280 |
| issn | 0143-3857 1469-4417 |
| language | eng |
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| source | Cambridge University Press Journals Complete |
| subjects | Lower bounds Original Article |
| title | Lower bound for the Perron–Frobenius degrees of Perron numbers |
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