Around Fekete's theorem
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911295577522176 |
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| author | Levenberg, Norm Londhe, Mayuresh |
| author_facet | Levenberg, Norm Londhe, Mayuresh |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06446 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Around Fekete's theorem Levenberg, Norm Londhe, Mayuresh Complex Variables Number Theory 11G50, 31A15 (primary), 11R06, 30C85 (secondary) 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. |
| title | Around Fekete's theorem |
| topic | Complex Variables Number Theory 11G50, 31A15 (primary), 11R06, 30C85 (secondary) |
| url | https://arxiv.org/abs/2404.06446 |