论文标题
有界程度的随机多项式的不可约性
Irreducibility of random polynomials of bounded degree
论文作者
论文摘要
众所周知，有界度$ d $的随机元积分多项式和在$ [-h，h] $中均匀和独立分布的积分系数在$ \ mathbb {z} $上是不可记录的，并且概率趋于$ 1 $ as $ h \ as $ h \ as $ h \ to \ suftty $。在本文中，我们给出了一个一般标准，用于保证在更一般的系数分布下保证相同的结论，从而使它们在任意集中不均匀且相关地分布。
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.
