论文标题
SATO-TATE分布的自动相关函数和符号字符的身份
Auto-correlation functions of Sato-Tate distributions and identities of symplectic characters
论文作者
论文摘要
属2曲线的SATO-TATE分布（猜想）描述了曲线上有理点数量的统计。在本文中，我们明确地计算了SATO-TATE分布属的自动相关函数，该属属2曲线是符号基团的不可减至特征的总和。我们的计算带来了涉及Symplectic Groups $ sp（200万）$ sp（200万）$ MATHBB Z y Mathbb Z _ {\ GE 1} $不可约的特征的家族，这对自己的权利有兴趣。
The Sato-Tate distributions for genus 2 curves (conjecturally) describe the statistics of numbers of rational points on the curves. In this paper, we explicitly compute the auto-correlation functions of Sato-Tate distributions for genus 2 curves as sums of irreducible characters of symplectic groups. Our computations bring about families of identities involving irreducible characters of symplectic groups $Sp(2m)$ for all $m \in \mathbb Z_{\ge 1}$, which have interest in their own rights.
