Irreducible polynomials of bounded height

Lior Bary-Soroker, Gady Kozma

Research output: Contribution to journalArticlepeer-review

Abstract

The goal of this paper is to prove that a random polynomial with independent and identically distributed random coefficients taking values uniformly in {1;::: ; 210} is irreducible with probability tending to 1 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 1.

Original languageEnglish
Pages (from-to)579-598
Number of pages20
JournalDuke Mathematical Journal
Volume169
Issue number4
DOIs
StatePublished - 2020

Funding

FundersFunder number
Jesselon Foundation
Israel Science Foundation1369/15, 952/14

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