Zeros ofL-functions attached to Maass forms
Zeros ofL-functions attached to Maass forms
复制标题
DOI：
10.1007/bf01159169
复制
发表时间：
1985-03
影响因子：
0.8
通讯作者：
C. Epstein;J. L. Hafner;P. Sarnak
中科院分区：
文献类型：
--
作者：
C. Epstein;J. L. Hafner;P. Sarnak
本文研究了PSL(2, 0)-自同构尖形（mass形）及其相关的Dirichlet级数。有两个主要结果。第一种方法使用实变量技术给出了狄利克雷级数形式的尖形的显式重建。这个表示在整个上半平面上都是有效的。第二种是用这种表示来说明狄利克雷级数在它的临界线上有许多零。这与黎曼ζ函数的Hardy-Littlewood结果类似。
This paper considers PSL (2, ℤ)-automorphic cusp forms (the Maass forms) and their associated Dirichlet series. There are two major results. The first uses real variable techniques to give an explicit reconstruction of the cusp form in terms of the Dirichlet series. This representation is valid in the entire upper half-plane. The second uses this representation to show that the Dirichlet series has many zeros on its critical line. This is the analogue of the Hardy-Littlewood result for the Riemann zeta function.