Irreducible polynomials of bounded height
Number Theory
2020-03-18 v2 Probability
Abstract
The goal of this paper is to prove that a random polynomial with i.i.d. random coefficients taking values uniformly in is irreducible with probability tending to as the degree tends to infinity. Moreover, we prove that the Galois group of the random polynomial contains the alternating group, again with probability tending to .
Cite
@article{arxiv.1710.05165,
title = {Irreducible polynomials of bounded height},
author = {Lior Bary-Soroker and Gady Kozma},
journal= {arXiv preprint arXiv:1710.05165},
year = {2020}
}
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