# 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}
}
• 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.
2 Citations
• Mathematics
• 2020
Let f(x) be a random integral polynomial of degree d ≥ 2 with coefficients uniformly and independently drawn from [−N,N ]. It is well known that the probability that f(x) is irreducible over the
• Computer Science, Art
Transactions of the American Mathematical Society
• 2023
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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