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December 2019 Irreducibility of random polynomials of large degree
Emmanuel Breuillard, Péter P. Varjú
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Acta Math. 223(2): 195-249 (December 2019). DOI: 10.4310/ACTA.2019.v223.n2.a1

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.

Funding Statement

E. B. acknowledges support from ERC Grant no. 617129 ‘GeTeMo’. P. V. acknowledges support from the Royal Society.

Citation

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Emmanuel Breuillard. Péter P. Varjú. "Irreducibility of random polynomials of large degree." Acta Math. 223 (2) 195 - 249, December 2019. https://doi.org/10.4310/ACTA.2019.v223.n2.a1

Information

Received: 31 October 2018; Published: December 2019
First available in Project Euclid: 16 April 2020

zbMATH: 07146625
MathSciNet: MR4047924
Digital Object Identifier: 10.4310/ACTA.2019.v223.n2.a1

Subjects:
Primary: 11C08
Secondary: 11M41, 60J10

Rights: Copyright © 2019 Institut Mittag-Leffler

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Vol.223 • No. 2 • December 2019
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