The Riemann Zeta-Function and Hecke Congruence Subgroups. II
The Riemann Zeta-Function and Hecke Congruence Subgroups. II
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黎曼 Zeta 函数和赫克同余子群。
DOI：
10.11346/cstj.2009.119_29
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
Y. Motohashi
中科院分区：
文献类型：
--
作者：
Y. Motohashi
这是对我们1994年9月以来未发表的旧文件的重写，关于黎曼ζ函数的四次方矩对权值的显式谱分解，权值是狄利克雷多项式的平方。在这种情况下，我们增加了与任意Hecke同余子群（第15节）相关的广义Kloosterman和的明确处理，这可能具有独立的兴趣。在我们讨论的最后（第36节），我们提出了一些关于双曲拉普拉斯特征值分布的问题，这些问题似乎与黎曼ζ函数的六次方矩的性质有关。这项工作的内容于2007年10月18日在RIMS京都大学的一个研讨会上发表。
This is a rework of our old file, which has been left unpublished since September 1994, on an explicit spectral decomposition of the fourth power moment of the Riemann zeta-function against a weight which is the square of a Dirichlet polynomial. At this occasion we add an explicit treatment of generalized Kloosterman sums associated with arbitrary Hecke congruence subgroups (Section 15), which might have an independent interest. At the end (Section 36) of our discussion, we set out a few problems on the distribution of eigenvalues of the hyperbolic Laplacian, which appear to us to be related to the nature of the sixth power moment of the Riemann zeta-function. The contents of this work were presented in a worshop at RIMS Kyoto University on October 18, 2007.
In this second version, some corrections are made in the part on generalized Kloosterman sums, and in Addendum a mention is made concerning a recent work by C.P. Hughes and M.P. Young (0709.2345).