论文标题
SATO-TATE序列的较高的矩相关函数
Higher moments of the pair correlation function for Sato-Tate sequences
论文作者
论文摘要
在\ cite {bs}中，Balasubramanyam和第二名的作者得出了对Hecke Angles的第一刻，该角度的第一瞬间，位于$ [0,1] $的小型$ [0,1] $中，平均与$ k $的Hecke Newforms相比，与$γ_0（n）$相比。本文的目的是研究该对相关函数的较高时刻。对于整数$ r \ geq 2 $，我们以$ r $ th的功率矩呈现界限。我们将这些界限应用于第二和第三矩计算中的较低订单误差项。结果，可以获得适当小的间隔，以及在适当的生长条件下，对于Hecke Newforms家族的大小，可以获得该对相关函数的第二和第三矩的收敛性。
In \cite{BS}, Balasubramanyam and the second named author derived the first moment of the pair correlation function for Hecke angles lying in small subintervals of $[0,1]$ upon averaging over large families of Hecke newforms of weight $k$ with respect to $Γ_0(N)$. The goal of this article is to study higher moments of this pair correlation function. For an integer $r \geq 2$, we present bounds for its $r$-th power moments. We apply these bounds to record lower order error terms in the computation of the second and third moments. As a result, one can obtain the convergence of the second and third moments of this pair correlation function for suitably small intervals, and under appropriate growth conditions for the size of the families of Hecke newforms.
