Irreducibility of random polynomials of bounded degree

@article{Pham2020IrreducibilityOR,
  title={Irreducibility of random polynomials of bounded degree},
  author={Huy-Tuan Pham and Max Wenqiang Xu},
  journal={arXiv: Number Theory},
  year={2020}
}
  • H. PhamM. Xu
  • Published 24 February 2020
  • Mathematics
  • arXiv: Number Theory
It is known that random monic integral polynomials of bounded degree $d$ and integral coefficients distributed uniformly and independently in $[-H,H]$ are irreducible over $\mathbb{Z}$ with probability tending to $1$ as $H\to \infty$. In this paper, we prove that the same conclusion holds under much more general distributions of the coefficients, allowing them to be dependently and nonuniformly distributed. 

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It is established that the number of such polynomials, monic and irreducible with integer coefficients in <inline-formula content-type="math/mathml" xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n greater-than-or-slanted-equals 3") is established.

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