论文标题
随机矩阵的特征多项式
The characteristic polynomial of a random matrix
论文作者
论文摘要
通过$ \ {\ pm1 \} $独立于绘制条目（或在$ \ Mathbf {z} $中）形成$ n \ times n $矩阵（或另一个固定的非平地有限支持的分布），让$ ϕ $为特征polynomial。有条件地在扩展的Riemann假设上，具有高概率$ ϕ $是不可约的，而$ \ mathrm {gal}（ϕ）\ geq a_n $。
Form an $n \times n$ matrix by drawing entries independently from $\{\pm1\}$ (or another fixed nontrivial finitely supported distribution in $\mathbf{Z}$) and let $ϕ$ be the characteristic polynomial. Conditionally on the extended Riemann hypothesis, with high probability $ϕ$ is irreducible and $\mathrm{Gal}(ϕ) \geq A_n$.
