The group of rational points on the unit circle
单位圆上有理点的群结构 这是一个交换群, 其加法定义为 \[ (x, y)\oplus (z, w) = (xz − wy, xw + yz).\]
The group of rational points on the unit circle Read MoreTag: elliptic curves
Manjul Bhargava: The Musical, Magical Number Theorist
Manjul Bhargava, 昨天上午在第二十七届国际数学家大会(ICM 2014)开幕式上, 从韩国总统朴槿惠手中接过菲尔兹奖章. References Erica Klarreich, The Musical, Magical Number Theorist, August 12, 2014
Manjul Bhargava: The Musical, Magical Number Theorist Read MoreManjul Bhargava, the BSD conjecture and Fields medal
Conjecture There exist elliptic curve groups \(E(\Bbb Q)\) of arbitrarily large rank. 用 \(r\) 表示 \(\Bbb Q\) 上的椭圆曲线 \(E\) 的秩—the rank of the Mordell–Weil group \(E(\Bbb Q)\). 一个悬而未决的著名难题是: \(r\) 是否可以任意大? Martin-McMillen 2000 …
Manjul Bhargava, the BSD conjecture and Fields medal Read More