Mathematical Sciences: L-functions, Exponential Sums, and Applications of Automorphic Theory to Diophantine Problems

数学科学：L 函数、指数和以及自守理论在丢番图问题中的应用

• 批准号: 9202022
• 负责人: Henryk Iwaniec
• 金额: $ 22.5万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-01 至 1995-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9202022&HistoricalAwards=false
• 关键词: Mathematical; Sciences; functions; Exponential; Sums

This grant supports the research of Professor H. Iwaniec and W. Duke to work on several problems connected with analytic number theory and automorphic forms. In particular, they will attempt to establish analytic continuation of L-functions derived from the product of two L-functions which have functional equations. They will also attempt to establish the equidistribution of roots of quadratic congruences to prime module and finally they will study generalization of the Linnik problem about lattice points in family of varieties. 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.

该基金支持H教授的研究。伊万涅茨和 W.杜克致力于与分析有关的几个问题 数论和自守形式 特别是，他们将 试图建立解析延拓的L-函数导出 从两个L-函数的乘积中， 方程 他们还将试图建立 素数的二次同余根的等分布 模块，最后他们将研究Linnik的推广 簇族中的格点问题。 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。