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Counting Perron numbers by absolute value
Author(s) -
Calegari Frank,
Huang Zili
Publication year - 2017
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms.12061
Subject(s) - mathematics , algebraic number , absolute (philosophy) , distribution (mathematics) , quadratic integer , entropy (arrow of time) , dimension (graph theory) , discrete mathematics , real number , combinatorics , mathematical analysis , philosophy , physics , epistemology , quantum mechanics
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 ].