论文标题
有效的晶格点的等均分布
Effective equidistribution of lattice points in positive characteristic
论文作者
论文摘要
给定有限字段的全球函数字段$ k $的位置$ω$，并带有相关的仿射功能环$r_Ω$和完成$k_Ω$，本文的目的是给出有效的联合等均衡性结果，以重新授权的原始晶格点$（a，b）在{r_Ω}}^2 $ for for {2 $ for {2 $ e}^2 $}^2 $}^2 $}^2 $}^2 $}^2 $}^2 $}^2 $}^2 $}^2^2^^2^^2^^2^^2^^2^^2^2^2 $} $ ax+by = 1 $。主要工具是Goronik和Nevo的技术，用于计算全面的子集家族中的晶格点。这给出了Nevo结果的积极特征的更尖锐的类似物，也是第一位在$ \ zz^2 $中对原始晶格点等分的作者。
Given a place $ω$ of a global function field $K$ over a finite field, with associated affine function ring $R_ω$ and completion $K_ω$, the aim of this paper is to give an effective joint equidistribution result for renormalized primitive lattice points $(a,b)\in {R_ω}^2$ in the plane ${K_ω}^2$, and for renormalized solutions to the gcd equation $ax+by=1$. The main tools are techniques of Goronik and Nevo for counting lattice points in well-rounded families of subsets. This gives a sharper analog in positive characteristic of a result of Nevo and the first author for the equidistribution of the primitive lattice points in $\ZZ^2$.
