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<p>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.</p>

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Around Fekete’s Theorem

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月3日

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  • Norm Levenberg,
  • Mayuresh Londhe

摘要

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.