Low lying zeros of families of L-functions
Low lying zeros of families of L-functions
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DOI：
10.1007/bf02698741
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发表时间：
1999-01
期刊：
影响因子：
--
通讯作者：
H. Iwaniec;Wenzhi Luo;P. Sarnak
中科院分区：
文献类型：
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作者：
H. Iwaniec;Wenzhi Luo;P. Sarnak
在Iwaniec-Sarnak [IS]中，GL族的中心值的非零百分比。2自守L-函数。本文研究了这类L-函数族在s= y（即中心点）处或附近的零点分布。与[IS]不同，本文的结果大多是条件性的，依赖于广义黎曼假设（GRH）。Katz Sarnak [KS 1，KS 2]最近研究了某些族J^的L-函数在s= j附近的密度和零点分布。出现的哲学和猜想断言，对于此类族，当我们按其导体对L函数进行排序时（见下文），低位零点的分布为
In Iwaniec-Sarnak [IS] the percentage of nonvanishing of central values of families of GL. 2 automorphic L-functions was investigated. In this paper we examine the distribution of zeros which are at or near s= y (that is the central point) for such families of L-functions. Unlike [IS], most of the results in this paper are conditional, depending on the generalized Riemann Hypothesis (GRH). It is by no means obvious, but on the other hand not surprising, that this allows us to obtain sharper results on the nonvanishing.The density and the distribution of zeros near s= j for the L-functions of certain families J^ have been studied recently in Katz-Sarnak [KS1, KS2]. The philosophy and conjectures which emerge assert that for such families, the distributions of the low lying zeros, when we order the L-functions by their conductors (see below), are