Form an n × n matrix by drawing entries independently from {±1} (or another fixed nontrivial finitely supported distribution in Z) and let φ be the characteristic polynomial. We show, conditionally on the extended Riemann hypothesis, that with high probability φ is irreducible and Gal(φ) ≥ A_n.

中文翻译：

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随机矩阵的特征多项式

通过独立于 {±1}（或Z中的另一个固定非平凡有限支持分布）绘制条目来形成n × n矩阵，并令φ为特征多项式。我们在扩展黎曼假设的条件下证明了φ是不可约的且 Gal( φ ) ≥ A _n的概率很高。