Year: 2026
Type: preprint
Abstract: We consider probability measures on compact subsets of the complex plane arising as limiting distributions of Galois conjugates of certain algebraic integers. These measures are characterized by infinitely many integral inequalities, one for each nonzero integer polynomial. We study a broad family of measures given by particular convex combinations of harmonic and equilibrium measures. We then show that, for measures in this family, it suffices to verify two conditions to guarantee all the required inequalities. Under additional arithmetic constraints on the underlying compact sets, we further show that the infinite collection of inequalities is equivalent to checking the inequalities associated with two explicitly specified integer polynomials.
Source: arXiv (Cornell University)
Author: Londhe, Mayuresh
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G133517437
OpenAlex ID: W7208744949