Irreducible polynomials of bounded height

Lior Bary-Soroker; Gady Kozma

doi:https://doi.org/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

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https://doi.org/10.1215/00127094-2019-0047

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

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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.

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JO - Duke Mathematical Journal

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Irreducible polynomials of bounded height

Abstract

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