Mod‐Gaussian convergence and the value distribution of ζ(½ + it) and related quantities
Mod‐Gaussian convergence and the value distribution of ζ(½ + it) and related quantities
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DOI：
10.1112/jlms/jds003
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发表时间：
2009-12
期刊：
影响因子：
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通讯作者：
Emmanuel Kowalski;A. Nikeghbali
中科院分区：
文献类型：
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作者：
Emmanuel Kowalski;A. Nikeghbali
在模高斯收敛的背景下，正如我们之前与Jacod的工作中所定义的那样，我们获得了随机向量序列的局部概率的渐近公式和下界，在这个意义上近似高斯，协方差矩阵增加。这是出于猜想的密度的一组值的黎曼zeta函数的临界线。我们得到了这一事实的证据，并得出了紧致经典群中随机矩阵的无条件结果，以及有限域上某些L-函数族的无条件结果。
In the context of mod‐Gaussian convergence, as defined previously in our work with Jacod, we obtain asymptotic formulas and lower bounds for local probabilities for a sequence of random vectors which are approximately Gaussian in this sense, with increasing covariance matrix. 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.