Quantitative versions of the joint distributions of Hecke eigenvalues
Quantitative versions of the joint distributions of Hecke eigenvalues
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DOI：
10.1016/j.jnt.2016.05.011
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发表时间：
2016-12
影响因子：
0.7
通讯作者：
H. Tang;Yingnan Wang
中科院分区：
文献类型：
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作者：
H. Tang;Yingnan Wang
2009年，Omar和Mazhouda证明了as k→∞，{λf(P2)：f∈Hk}和{λf(P3)：f∈Hk}分别关于某些测度是均匀分布的，其中Hk是S 2(Z)的所有权为k的正规化本原全纯尖形的集合。在本文中，我们得到了Omar和Mazhouda结果的一个定量版本。此外，我们还发现{λf(P4)：f∈Hk}和{λf(P R)−λf(p r−2)：f∈Hk和r≥2}分别服从k→∞分布规律，并得到了这些分布的定量形式。在Maass尖点形式的背景下，我们建立了类似的结果。
Abstract In 2009, Omar and Mazhouda proved that as k→∞,{λ f (p 2): f∈ H k} and {λ f (p 3): f∈ H k} are equidistributed with respect to some measures respectively, where H k is the set of all the normalized primitive holomorphic cusp forms of weight k for S L 2 (Z). In this paper, we obtain a quantitative version of Omar and Mazhouda's result. Moreover, we find out that {λ f (p 4): f∈ H k} and {λ f (p r)− λ f (p r− 2): f∈ H k and r≥ 2} follow some nice distribution laws respectively as k→∞ and get quantitative versions of these distributions. In the context of Maass cusp forms, we establish analogous results.