2021/11/24 by Alexander Smith, Smith, Alexander
Computer Science · Mathematics · #11G25 (Secondary) #11R06 (Primary) 11G10 #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2111.12660
openalex publication_date 2021/11/24 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
Given a compact subset Σ of the real numbers obeying some technical conditions, we consider the set of algebraic integers whose conjugates all lie in Σ. The distribution of conjugates of such an integer defines a probability measure on Σ; our main result gives a necessary and sufficient condition for a given probability measure on Σ to be the limit of some sequence of distributions of conjugates. As one consequence, we show there are infinitely many totally positive algebraic integers α with tr(α) < 1.89831⋅ deg(α). We also show how this work can be applied to find simple abelian varieties over finite fields with extreme point counts.