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PreprintCC BY 4.0arXiv

The Odlyzko-Poonen Conjecture on Irreducibility of Random Polynomials

  • Constantin Kogler
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Abstract

The Odlyzko-Poonen conjecture states that a monic polynomial of constant coefficient $1$ and with remaining coefficients chosen independently and uniformly from {0,1 } is irreducible over the rational numbers with probability tending to one as the degree tends to infinity. We prove the Odlyzko-Poonen conjecture unconditionally.

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Cite

BibTeXRIS
BibTeX
@misc{kogler2026odlyzkopoonen,
  title = {{The Odlyzko-Poonen Conjecture on Irreducibility of Random Polynomials}},
  author = {Constantin Kogler},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.26771},
  eprint = {2609.26771},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26771},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Odlyzko-Poonen Conjecture on Irreducibility of Random Polynomials
AU  - Constantin Kogler
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.26771
UR  - https://arxiv.org/abs/2609.26771
AB  - The Odlyzko-Poonen conjecture states that a monic polynomial of constant coefficient $1$ and with remaining coefficients chosen independently and uniformly from {0,1 } is irreducible over the rational numbers with probability tending to one as the degree tends to infinity. We prove the Odlyzko-Poonen conjecture unconditionally.
ER  -