Mean values of L-functions and symmetry
Mean values of L-functions and symmetry
复制标题
L 函数和对称性的平均值
DOI：
10.1155/s1073792800000465
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发表时间：
1999
影响因子：
1
通讯作者：
D. Farmer
中科院分区：
文献类型：
--
作者：
J. Conrey;D. Farmer
最近，Katz和Sarnak引入了l函数族的对称群的概念，他们给出了有力的证据，证明对称群支配着l函数的零点分布的许多性质。我们考虑了l -函数的均值和l -函数的平滑均方，并找到了它们也受对称群支配的证据。我们使用Keating和Snaith最近的工作来给出这些平均值的完整描述。我们找到了与Barnes-Vign\ \ eras $\Gamma_2$ $-函数和一组自相似函数的联系。
Recently Katz and Sarnak introduced the idea of a symmetry group attached to a family of L-functions, and they gave strong evidence that the symmetry group governs many properties of the distribution of zeros of the L-functions. We consider the mean-values of the L-functions and the mollified mean-square of the L-functions and find evidence that these are also governed by the symmetry group. We use recent work of Keating and Snaith to give a complete description of these mean values. We find a connection to the Barnes-Vign\'eras $\Gamma_2$-function and to a family of self-similar functions.