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Counting Perron numbers by absolute value. (English) Zbl 1427.11109

Summary: We count various classes of algebraic integers of fixed degree by their largest absolute value. The classes of integers considered include all algebraic integers, Perron numbers, totally real integers, and totally complex integers. We give qualitative and quantitative results concerning the distribution of Perron numbers, answering in part a question of Thurston [’Entropy in dimension one’, to appear in the Proceedings of the Banff Conference on Frontiers in Complex Dynamics].

MSC:

11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measure
11R09 Polynomials (irreducibility, etc.)
11C08 Polynomials in number theory
30C10 Polynomials and rational functions of one complex variable
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