Irreducibility of Littlewood Polynomials of Special Degrees
Abstract Let $f$ be sampled uniformly at random from the set of degree $n$ polynomials whose coefficients lie in $\{ \pm 1\}$. 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 $$ \begin{align*}& \limsup_{n \to \infty} \mathbb{P}(f \textrm{ is irreducible}) = 1. \end{align*} $$
Authors
- Bjorn Poonen (ORCID: https://orcid.org/0000-0002-8593-2792)
- Lior Bary‐Soroker (ORCID: https://orcid.org/0000-0002-1303-247X)
- Gady Kozma
- David Hokken
Institutions
- Tel Aviv University (IL)
- Utrecht University (NL)
- Weizmann Institute of Science (IL)
- Massachusetts Institute of Technology (US)
Publication Details
- Journal
- International Mathematics Research Notices
- Published
- 2025-10-11
- DOI
- https://doi.org/10.1093/imrn/rnaf326
- Primary Topic
- Algebraic Geometry and Number Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- Nederlandse Organisatie voor Wetenschappelijk Onderzoek
- Tel Aviv University