Irreducibility of Littlewood polynomials of special degrees
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914631431225344 |
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| author | Bary-Soroker, Lior Hokken, David Kozma, Gady Poonen, Bjorn |
| author_facet | Bary-Soroker, Lior Hokken, David Kozma, Gady Poonen, Bjorn |
| contents | 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 $$\limsup_{n \to \infty} \mathbb{P}(f \text{ is irreducible}) = 1.$$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_04878 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Irreducibility of Littlewood polynomials of special degrees Bary-Soroker, Lior Hokken, David Kozma, Gady Poonen, Bjorn Number Theory Probability 11R09 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 $$\limsup_{n \to \infty} \mathbb{P}(f \text{ is irreducible}) = 1.$$ |
| title | Irreducibility of Littlewood polynomials of special degrees |
| topic | Number Theory Probability 11R09 |
| url | https://arxiv.org/abs/2308.04878 |