Translator Disclaimer
15 March 2020 Irreducible polynomials of bounded height
Lior Bary-Soroker, Gady Kozma
Duke Math. J. 169(4): 579-598 (15 March 2020). DOI: 10.1215/00127094-2019-0047

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.

Citation

Download Citation

Lior Bary-Soroker. Gady Kozma. "Irreducible polynomials of bounded height." Duke Math. J. 169 (4) 579 - 598, 15 March 2020. https://doi.org/10.1215/00127094-2019-0047

Information

Received: 6 November 2017; Revised: 25 April 2019; Published: 15 March 2020
First available in Project Euclid: 10 January 2020

zbMATH: 07198462
MathSciNet: MR4072635
Digital Object Identifier: 10.1215/00127094-2019-0047

Subjects:
Primary: 11R09
Secondary: 12E05, 26C05

Rights: Copyright © 2020 Duke University Press

JOURNAL ARTICLE
20 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.169 • No. 4 • 15 March 2020
Back to Top