【数学学院】p-adic equidistribution of CM points and applications

报告题目：

p-adic equidistribution of CM points and applications

报告人：Daniel Disegni

报告人单位：Université Paris-Sud

报告时间：8月9日（周四）上午10:00-11:00

报告地点：数学学院东302（2）

邀请人：张起帆

Abstract:

Let $X$ be a modular curve. It is a curve over the integers, whose complex points are a quotient of the (compactified) Poincaré upper-half

plane $H$ by a subgroup of $SL(2,Z)$. The curve $X$ has a natural supply of (almost) rational points called CM points. Following Heegner, 

these are useful to construct rational solutions to cubic equations in two variables (elliptic curves).

Let $z_n$ be a sequence of CM points of increasing “p-adic complexity” for some prime $p$. A theorem of Duke says that the images of the

$z_n$ in $X(C)$ equidistribute to the quotient of the Haar measure on $H$. A theorem of Cornut—Vatsal describes the equidistribution 

properties of the $z_n$ modulo primes different from $p$. I will talk about a p-adic equidistribution result for the $z_n$, and sketch

its application to the study of Heegner’s solutions.

来源链接：http://math.scu.edu.cn/info/1062/3624.htm