论文标题
随机欧拉产品的概率密度功能，用于自动形态$ l $ functions
Probability density functions attached to random Euler products for automorphic $L$-functions
论文作者
论文摘要
在本文中，我们研究了整体原始尖端形式的$ l $ functions的价值分布。我们将此类自动形态$ L $功能与称为Random Euler产品的概率模型相关联。首先，我们证明了随机欧拉产品附加的概率密度函数的存在。然后，自动形态$ l $ - 功能的各种平均值表示为涉及密度函数的积分。此外，我们估计自动形态$ l $ functions的值的分布与随机欧拉产品的值之间的差异。
In this paper, we study the value-distributions of $L$-functions of holomorphic primitive cusp forms in the level aspect. We associate such automorphic $L$-functions with probabilistic models called the random Euler products. First, we prove the existence of probability density functions attached to the random Euler products. Then various mean values of automorphic $L$-functions are expressed as integrals involving the density functions. Moreover, we estimate the discrepancies between the distributions of values of automorphic $L$-functions and those of the random Euler products.
