Around Fekete's theorem
Complex Variables
2025-12-02 v2 Number Theory
Abstract
A classical result of Fekete gives necessary conditions on a compact set in the complex plane so that it contains infinitely many sets of conjugate algebraic integers. For such sets, we demonstrate the existence of a sequence of algebraic integers such that most of their conjugates eventually lie near the set, while maintaining a bound on heights. Finally, we examine properties satisfied by the limiting distribution of a sequence of algebraic numbers.
Cite
@article{arxiv.2404.06446,
title = {Around Fekete's theorem},
author = {Norm Levenberg and Mayuresh Londhe},
journal= {arXiv preprint arXiv:2404.06446},
year = {2025}
}
Comments
Final version; to appear in Potential Analysis