Quantitative version of the joint distribution of eigenvalues of the Hecke operators
Quantitative version of the joint distribution of eigenvalues of the Hecke operators
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DOI：
10.1016/j.jnt.2011.05.014
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发表时间：
2011-12
影响因子：
0.7
通讯作者：
Y. Lau;Yingnan Wang
中科院分区：
文献类型：
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作者：
Y. Lau;Yingnan Wang
最近，Murty 和 Sinha 证明了原始全纯尖点形式空间上 Hecke 算子特征值的 Serre 等分布定理的有效/定量版本。在原始马斯形式的背景下，萨纳克找出了类似的联合分布。在本文中，我们证明了萨纳克定理的定量版本，该定理给出了收敛速度的明确估计。同样的结果也适用于全纯尖点形式的情况。
Recently, Murty and Sinha proved an effective/quantitative version of Serreʼs equidistribution theorem for eigenvalues of Hecke operators on the space of primitive holomorphic cusp forms. In the context of primitive Maass forms, Sarnak figured out an analogous joint distribution. In this paper, we prove a quantitative version of Sarnakʼs theorem that gives explicitly estimate on the rate of convergence. The same result also holds for the case of holomorphic cusp forms.