论文标题
随机矩阵理论和$ l $ functions的时刻
Random matrix theory and moments of moments of $L$-functions
论文作者
论文摘要
我们给出了随机符号和正交矩阵的特征多项式矩的矩矩的分析证明。因此，我们获得了先前由Assiotis，Bailey和Keating发现的前列顺序系数的替代积分表达式。我们还讨论了Bailey和Keating的猜想，以与符号和正交对称的L功能的相应力矩。具体来说，我们表明，这些猜想是从康雷，农民，基廷，鲁宾斯坦和斯诺伊思的转移瞬间开始的。
We give an analytic proof of the asymptotic behaviour of the moments of moments of the characteristic polynomials of random symplectic and orthogonal matrices. We therefore obtain alternate, integral expressions for the leading order coefficients previously found by Assiotis, Bailey and Keating. We also discuss the conjectures of Bailey and Keating for the corresponding moments of moments of L-functions with symplectic and orthogonal symmetry. Specifically, we show that these conjectures follow from the shifted moments conjecture of Conrey, Farmer, Keating, Rubinstein and Snaith.
