In this paper, we give an analytic proof of the asymptotic behavior 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.

中文翻译：

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随机矩阵理论和 L 函数矩的矩

本文给出了随机辛正交矩阵特征多项式矩矩的渐近行为的解析证明。因此，我们获得了 Assiotis、Bailey 和 Keating 先前发现的前导系数的替代积分表达式。我们还讨论了贝利和基廷对 的对应矩的猜想$L$-具有辛对称性和正交对称性的函数。具体来说，我们表明这些猜想源自康利、法默、基廷、鲁宾斯坦和斯奈斯的移矩猜想。