## New constraints on the Galois configurations of algebraic integers in the complex plane

Vesselin Dimitrov

University of Toronto

June 11, 2020

Fekete (1923) discovered the notion of transfinite diameter while studying the possible configurations of Galois orbits of algebraic integers in the complex plane. Based purely on the fact that the discriminants of monic integer irreducible polynomials P(X)∈ℤ[X] are at least 1 in magnitude (since they are non-zero integers), he found that the incidences (,P) between these polynomials P(X) and compacts ⊂ℂ of transfinite diameter d()