关于整系数随机整系数多项式不可约的概率
On the probability of irreducibility of random polynomials with integer coefficients
摘要：
本文研究了整系数随机首一多项式在整数上不可约的概率的渐近性态。我们考虑的情况下，系数一起增长的随机多项式的程度。我们的主要结果是Konyagin在1999年证明的一个定理的推广。我们还推广了希尔伯特的不可约定理，并提出了一个类似的结果与中心二项式分布的系数。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
