Irreducible polynomials of bounded height

Lior Bary-Soroker; Gady Kozma

doi:10.1215/00127094-2019-0047

Irreducible polynomials of bounded height

Lior Bary-Soroker, Gady Kozma

Tel Aviv University, Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	579-598
Number of pages	20
Journal	Duke Mathematical Journal
Volume	169
Issue number	4
Early online date	10 Jan 2020
DOIs	https://doi.org/10.1215/00127094-2019-0047
State	Published - 15 Mar 2020

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1215/00127094-2019-0047

https://arxiv.org/abs/1710.05165License: Other

Cite this

@article{0050603c19e647eb8bb923345ff045de,

title = "Irreducible polynomials of bounded height",

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.",

author = "Lior Bary-Soroker and Gady Kozma",

note = "Publisher Copyright: {\textcopyright} 2020.",

year = "2020",

month = mar,

day = "15",

doi = "10.1215/00127094-2019-0047",

language = "الإنجليزيّة",

volume = "169",

pages = "579--598",

journal = "Duke Mathematical Journal",

issn = "0012-7094",

publisher = "Duke University Press",

number = "4",

}

TY - JOUR

T1 - Irreducible polynomials of bounded height

AU - Bary-Soroker, Lior

AU - Kozma, Gady

PY - 2020/3/15

Y1 - 2020/3/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85094742986&partnerID=8YFLogxK

U2 - 10.1215/00127094-2019-0047

DO - 10.1215/00127094-2019-0047

M3 - مقالة

SN - 0012-7094

VL - 169

SP - 579

EP - 598

JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

IS - 4

ER -

Irreducible polynomials of bounded height

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this