Irreducibility of Littlewood Polynomials of Special Degrees

Lior Bary-Soroker; David Hokken; Gady Kozma; Bjorn Poonen

doi:10.1093/imrn/rnaf326

Irreducibility of Littlewood Polynomials of Special Degrees

Lior Bary-Soroker
, David Hokken^*
, Gady Kozma
, Bjorn Poonen

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

Let f be sampled uniformly at random from the set of degree n polynomials whose coefficients lie in {±1}. A folklore conjecture, known to hold under GRH, states that the probability that f is irreducible tends to 1 as n goes to infinity. We prove unconditionally that (Formula presented).

Original language	English
Article number	rnaf326
Number of pages	5
Journal	International Mathematics Research Notices
Volume	2025
Issue number	21
DOIs	https://doi.org/10.1093/imrn/rnaf326
Publication status	Published - Nov 2025

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© The Author(s) 2025. Published by Oxford University Press.

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Irreducibility of Littlewood Polynomials of Special Degrees

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