English

Irreducible polynomials of bounded height

Number Theory 2020-03-18 v2 Probability

Abstract

The goal of this paper is to prove that a random polynomial with i.i.d. random coefficients taking values uniformly in {1,,210}\{1,\ldots, 210\} is irreducible with probability tending to 11 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 11.

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Cite

@article{arxiv.1710.05165,
  title  = {Irreducible polynomials of bounded height},
  author = {Lior Bary-Soroker and Gady Kozma},
  journal= {arXiv preprint arXiv:1710.05165},
  year   = {2020}
}

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R2 v1 2026-06-22T22:13:32.898Z