Mathematical Sciences: P-Adic Constructions on Elliptic Curves

鲁宾的作品在该地区的arithemetic椭圆曲线 以及伯奇和斯威纳顿-戴尔猜想 的主要重点 该建议是推广到模椭圆曲线一个新的 Rubin发现的方法，它使用p-adic L的特殊值， 构造秩为1的无穷级有理点的函数 椭圆曲线与复数乘法 这是数论领域的研究。 Number 理论开始于整数和问题，如 一个整数被另一个整数整除。 它是其中的 最古老的数学领域，它最初是追求 纯粹的美学原因。 然而，在过去的半个世纪里， 它已经成为开发新算法的重要工具， 计算机科学和新的电子纠错码。

Rubin works in the area of the arithemetic of elliptic curves and the Birch and Swinnerton-Dyer conjecture. The major focus of the proposal is to generalize to modular elliptic curves a new method discovered by Rubin which uses special values of p-adic L- functions to construct rational points of infinite order on rank-1 elliptic curves with complex multiplication. This is research in the field of number theory. Number theory starts with the whole numbers and questions such as the divisibility of one whole number by another. It is among the oldest fields of mathematics and it was originally pursued for purely aesthetic reasons. However, within the last half century, it has become an essential tool in developing new algorithms for computer science and new error correcting codes for electronics.