# 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} }

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

### Irreducibility and Galois Groups of Random Polynomials

- 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…

### Towards van der Waerden’s conjecture

- Computer Science, ArtTransactions 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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