$ζ(1/2+it)$的模高斯收敛性和value distribution及相关量
Mod-Gaussian convergence and the value distribution of $ζ(1/2+it)$ and related quantities
摘要：
在模高斯收敛的上下文中，如我们先前与J. Jacod的工作中所定义的，我们获得了一系列随机向量的局部概率的下界，这些向量近似为高斯，协方差增加。这是出于猜想的密度的一组值的黎曼ζ函数的临界线。我们获得了这一事实的证据，并得出无条件的结果，随机矩阵在紧凑的典型群，以及某些家庭的L-功能在有限域。
英文摘要：
In the context of mod-Gaussian convergence, as defined previously in our work with J. Jacod, we obtain lower bounds for local probabilities for a sequence of random vectors which are approximately Gaussian with increasing covariance. This is motivated by the conjecture concerning the density of the set of values of the Riemann zeta function on the critical line. We obtain evidence for this fact, and derive unconditional results for random matrices in compact classical groups, as well as for certain families of L-functions over finite fields.
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。
