Mathematical Sciences: RUI: Derivatives of L-Series for Elliptic Curves over Function Fields

数学科学：RUI：函数域上椭圆曲线的 L 级数导数

• 批准号: 9204307
• 负责人: David Dorman
• 金额: $ 3.86万
• 依托单位: Middlebury College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1994-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9204307&HistoricalAwards=false
• 关键词: Mathematical; Sciences; RUI; Derivatives; Series

This research is concerned with the arithmetic of function fields. The principal investigator will study Heegner points on modular curves with a view to proving an analog of the theorem of Gross and Zagier. 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.

本文研究的是函数场的算法问题。首席研究员将研究模曲线上的Heegner点，以证明Gross和Zagier定理的类比。这是数论领域的研究。数论从整数和诸如整数能被整数整除之类的问题开始。它是数学中最古老的领域之一，最初纯粹出于审美原因而追求它。然而，在过去的半个世纪里，它已经成为开发计算机科学新算法和电子学新纠错码的重要工具。