论文标题
Cusps的Canonical Green功能的界限
Bounds for canonical Green's functions at cusps
论文作者
论文摘要
令$γ$为富富奇族亚组。在为Arakelov理论建立与某些级别$ n $的一致性亚组与正整数$ n $相关的模块化曲线的Arakelov不变式时，Arakelov理论中的规范绿色功能与$ n $相关的渐近性。更确切地说，在已知情况下，某些尖cusp的规范格林的功能有助于分析部分的分析部分，以自我进行相对双重化的造纸条的自我交流。在本文中，我们证明了由散射常数，kronecker限制函数和组$γ$的Selberg Zeta函数界定的cofinite fuchsian子组的典范函数。然后，作为应用程序，我们证明了与$γ_0（n）$相关的规范绿色功能的渐近表达，对于任何正整数$ n $。
Let $Γ$ be a cofinite Fuchsian subgroup. The canonical Green's function associated with $Γ$ arises in Arakelov theory when establishing asymptotics for Arakelov invariants of the modular curve associated with some congruence subgroup of level $N$ with a positive integer $N$. More precisely, in the known cases, canonical Green's functions at certain cusps contribute to the analytic part of the asymptotics for the self-intersection of the relative dualizing sheaf. In this article, we prove canonical Green's function of a cofinite Fuchsian subgroup at cusps bounded by the scattering constants, the Kronecker limit functions, and the Selberg zeta function of the group $Γ$. Then as an application, we prove an asymptotic expression of the canonical Green's function associated with $Γ_0(N)$, for any positive integer $N$.
