Counting Perron Numbers by Absolute Value
Frank Calegari, Zili Huang
TL;DR
This paper investigates the distribution and enumeration of Perron numbers and related algebraic integers of fixed degree, providing new quantitative insights and answering longstanding questions in algebraic number theory.
Contribution
It offers novel counting formulas and distribution results for Perron numbers and other algebraic integers, expanding understanding of their properties and prevalence.
Findings
Quantitative counts of Perron numbers of fixed degree
Distribution patterns of algebraic integers by absolute value
Partial answers to Thurston's question on Perron numbers
Abstract
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 W. Thurston.
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Taxonomy
TopicsGeometry and complex manifolds · Mathematical Dynamics and Fractals · Data Management and Algorithms