On the mean values of L‐functions in orthogonal and symplectic families
On the mean values of L‐functions in orthogonal and symplectic families
复制标题
关于正交族和辛族中L函数的平均值
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
J. P. Keating
中科院分区：
文献类型：
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作者：
H. Bui;J. P. Keating
混合Euler-Hadamard乘积之前已经在其临界线上的Riemann zeta函数和Dirichlet L-函数中进行了研究，在随机矩阵理论的矩计算和连接的背景下。根据Katz-Sarnak分类，这些被认为是具有酉对称性的L-函数族。我们在这里扩展的形式主义，正交和辛对称的家庭。具体地说，我们建立了真实的二次Dirichlet L-函数和与权为2的本原Hecke特征形相关的L-函数的部分Euler和Hadamard乘积公式。然后，我们证明了这些部分产品的一些时刻的渐近公式，并作出一般的说明随机矩阵的特征多项式的时刻的结果的基础上。
Hybrid Euler–Hadamard products have previously been studied for the Riemann zeta function on its critical line and for Dirichlet L‐functions, in the context of the calculation of moments and connections with Random Matrix Theory. According to the Katz–Sarnak classification, these are believed to represent families of L‐function with unitary symmetry. We here extend the formalism to families with orthogonal and symplectic symmetry. Specifically, we establish formulae for real quadratic Dirichlet L‐functions and for the L‐functions associated with primitive Hecke eigenforms of weight 2 in terms of partial Euler and Hadamard products. We then prove asymptotic formulae for some moments of these partial products and make general conjectures based on results for the moments of characteristic polynomials of random matrices.