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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2304.10021 |
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Table of Contents:
- Given a compact subset $Σ\subset \mathbb{R}$ (or $\mathbb{C}$) with logarithmic capacity greater than zero, we construct an explicit family of probability measures supported on $Σ$ such that their closure is all the possible weak limit measures of complete sets of conjugate algebraic integers lying inside $Σ$. 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.