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arXiv · 2002.10554

Irreducibility of random polynomials of bounded degree

Huy Tuan Pham·Max Wenqiang Xu
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Abstract

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 give a general criterion for guaranteeing the same conclusion under much more general coefficient distributions, allowing them to be nonuniformly and dependently distributed over arbitrary sets.

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Huy Tuan Pham, Max Wenqiang Xu. 2021-07-20. Irreducibility of random polynomials of bounded degree. https://arxiv.org/abs/2002.10554

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