论文标题
关于随机多项式具有整数系数的概率
On the probability of irreducibility of random polynomials with integer coefficients
论文作者
论文摘要
在本文中，我们研究了与整数相对于整数不可还原的概率的渐近行为。我们考虑系数与随机多项式程度一起生长的情况。我们的主要结果是科尼亚金在1999年证明的定理的概括。我们还推广了希尔伯特的不可约性定理，并用中心的二项式分布系数对此结果进行了类似。
In this article we study asymptotic behavior of the probability that a random monic polynomial with integer coefficients is irreducible over the integers. We consider the cases where the coefficients grow together with the degree of the random polynomials. Our main result is a generalization of a theorem proved by Konyagin in 1999. We also generalize Hilbert's Irreducibility Theorem and present an analog of this result with centered Binomial distributed coefficients.
