Bryce Orloski

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math.NT2024

New Lower Bounds for the Schur-Siegel-Smyth Trace Problem

Bryce Joseph Orloski, Naser Talebizadeh Sardari, Alexander Smith

We derive and implement a new way to find lower bounds on the smallest limiting trace-to-degree ratio of totally positive algebraic integers and improve the previously best known b…

math.NT2024

Limiting distributions of conjugate algebraic integers

Bryce Joseph Orloski, Naser Talebizadeh Sardari

Let $I^£ \subset C$ be a compact subset of the complex plane, and $I^¼$ be a probability distribution on $I^£$ . We give necessary and sufficient conditions for $I^¼$ to be the…

math.NT2024

A quantitative converse of Fekete's theorem

Naser Talebizadeh Sardari, Bryce Joseph Orloski

Given a compact subset $I^£ \subset R$ (or $C$ ) with logarithmic capacity greater than zero, we construct an explicit family of probability measures supported on $Î…