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Lower bound for the Perron–Frobenius degrees of Perron numbers

Published online by Cambridge University Press:  14 January 2020

MEHDI YAZDI*
Affiliation:
University of Oxford, Mathematics, Andrew Wiles Building, Woodstock Road, OxfordOX2 6GG, UK email [email protected]

Abstract

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.

Type
Original Article
Copyright
© The Author(s) 2020. Published by Cambridge University Press

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