Non-vanishing of Geodesic Periods of Automorphic Forms

IF 2.5 1区 数学 Q1 MATHEMATICS
Petru Constantinescu, Asbjørn Christian Nordentoft
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引用次数: 0

Abstract

We prove that one hundred percent of the closed geodesic periods of a Hecke–Maaß cusp form for the modular group are non-vanishing when ordered by length. We present applications to the non-vanishing of central values of Rankin–Selberg \(L\)-functions. Similar results for holomorphic forms for general Fuchsian groups of finite covolume with a cusp are also obtained, as well as results towards normal distribution. Our new key ingredient is to relate the distributions of closed geodesic periods and vertical line integrals via graph theory.

自同构形式测地线周期的不消失性
证明了模群的hecke - maasus尖形的封闭测地周期在按长度排序时100%不消失。给出了Rankin-Selberg \(L\) -函数中心值不消失的应用。对于一般带尖的有限协体积的Fuchsian群的全纯形式也得到了类似的结果,并得到了正态分布的结果。我们新的关键成分是通过图论将封闭测地线周期和垂直线积分的分布联系起来。
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来源期刊
CiteScore
3.70
自引率
4.50%
发文量
34
审稿时长
6-12 weeks
期刊介绍: Geometric And Functional Analysis (GAFA) publishes original research papers of the highest quality on a broad range of mathematical topics related to geometry and analysis. GAFA scored in Scopus as best journal in "Geometry and Topology" since 2014 and as best journal in "Analysis" since 2016. Publishes major results on topics in geometry and analysis. Features papers which make connections between relevant fields and their applications to other areas.
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