A quantitative converse of Fekete's theorem
| Autor: | Sardari, Naser Talebizadeh, Orloski, Bryce Joseph |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | Given a compact subset $\Sigma \subset \mathbb{R}$ (or $\mathbb{C}$) with logarithmic capacity greater than zero, we construct an explicit family of probability measures supported on $\Sigma$ such that their closure is all the possible weak limit measures of complete sets of conjugate algebraic integers lying inside $\Sigma$. We give an asymptotic formula for the number of algebraic integers with given degree and prescribed distribution. We exploit the algorithmic nature of our approach to give a family of upper bounds that converges to the smallest limiting trace-to-degree ratio of totally positive algebraic integers and improve the best previously known upper bound on the Schur-Siegel-Smyth trace problem to 1.8216. Comment: arXiv admin note: text overlap with arXiv:2302.02872 |
| Databáze: | arXiv |
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