The Sixth Power Moment of Dirichlet L-Functions
The Sixth Power Moment of Dirichlet L-Functions
复制标题
狄利克雷 L 函数的六次幂矩
DOI：
10.1007/s00039-012-0191-6
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发表时间：
2007
影响因子：
2.2
通讯作者：
K. Soundararajan
中科院分区：
文献类型：
--
作者：
J. Conrey;J. Conrey;H. Iwaniec;K. Soundararajan
本文证明了Dirichlet L-函数在所有本原特征标χ（mod q）上（q ≤ Q）和临界线上的六阶矩的一个公式，并且具有省电的性质.我们的公式完全符合随机矩阵理论的预测。特别地，常数42作为首阶项中的因子出现，与黎曼ζ函数的六阶矩的预测完全相同。
We prove a formula, with power savings, for the sixth moment of Dirichlet L- functions averaged over all primitive characters χ (mod q) with q ≤ Q, and over the critical line. Our formula agrees precisely with predictions motivated by random matrix theory. In particular, the constant 42 appears as a factor in the leading order term, exactly as is predicted for the sixth moment of the Riemann zeta-function.