An explicit trace formula of Jacquet-Zagier type for Hilbert modular forms
An explicit trace formula of Jacquet-Zagier type for Hilbert modular forms
复制标题
希尔伯特模形式的Jacquet-Zagier型显式迹公式
DOI：
10.1016/j.jfa.2018.09.009
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发表时间：
2018
影响因子：
1.7
通讯作者：
Masao Tsuzuki
中科院分区：
文献类型：
--
作者：
Shingo Sugiyama;Masao Tsuzuki
给出了具有固定权和无平方因子水平的全纯Hilbert尖点型的伴随L-函数的平均值的一个精确公式，它是已知的SL 2（Z）上椭圆尖点型情形的Zagier公式的推广.作为应用，我们证明了在由伴随L-函数的值构成的系综中，具有固定权和不断增长的无平方级的Hilbert尖点形式的Satake参数是等分布的.
We give an exact formula of the average of adjoint L-functions of holomorphic Hilbert cusp forms with a fixed weight and a square-free level, which is a generalization of Zagier's formula known for the case of elliptic cusp forms on SL 2 (Z). As an application, we prove that the Satake parameters of Hilbert cusp forms with a fixed weight and with growing square-free levels are equidistributed in an ensemble constructed by values of the adjoint L-functions.