Irreducibility of random polynomials of large degree
Number Theory
2022-08-25 v2 Probability
Abstract
We consider random polynomials with independent identically distributed coefficients with a fixed law. Assuming the Riemann hypothesis for Dedekind zeta functions, we prove that such polynomials are irreducible and their Galois groups contain the alternating group with high probability as the degree goes to infinity. This settles a conjecture of Odlyzko and Poonen conditionally on RH for Dedekind zeta functions.
Keywords
Cite
@article{arxiv.1810.13360,
title = {Irreducibility of random polynomials of large degree},
author = {Emmanuel Breuillard and Péter P. Varjú},
journal= {arXiv preprint arXiv:1810.13360},
year = {2022}
}
Comments
50 pages, this is the accepted version for publication in Acta Math., minor changes and corrections based on referees' reports