{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/limiting-distributions-of-conjugate-algebraic","title":"Limiting distributions of conjugate algebraic integers","arxiv_id":"2302.02872","date":"2023-02-06","proceeding":null,"authors":["Bryce Joseph Orloski","Naser Talebizadeh Sardari"],"abstract":"Let $\\Sigma \\subset \\mathbb{C}$ be a compact subset of the complex plane, and $\\mu$ be a probability distribution on $\\Sigma$. We give necessary and sufficient conditions for $\\mu$ to be the weak* limit of a sequence of uniform probability measures on a complete set of conjugate algebraic integers lying eventually in any open set containing $\\Sigma$. Given $n\\geq 0$, any probability measure $\\mu$ satisfying our necessary conditions, and any open set $D$ containing $\\Sigma$, we develop and implement a polynomial time algorithm in $n$ that returns an integral monic irreducible polynomial of degree $n$ such that all of its roots are inside $D$ and their root distributions converge weakly to $\\mu$ as $n\\to \\infty$. We also prove our theorem for $\\Sigma\\subset \\mathbb{R}$ and open sets inside $\\mathbb{R}$ that recovers Smith's main theorem \\cite{Smith} as special case. Given any finite field $\\mathbb{F}_q$ and any integer $n$, our algorithm returns infinitely many abelian varieties over $\\mathbb{F}_q$ which are not isogenous to the Jacobian of any curve over $\\mathbb{F}_{q^n}$.","url_abs":"https://arxiv.org/abs/2302.02872v2","url_pdf":"https://arxiv.org/pdf/2302.02872v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"limiting-distributions-of-conjugate-algebraic","repo_url":"https://github.com/Bryce-Orloski/Limiting-Distributions-of-Conjugate-Algebraic-Integers-Applications","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}