Mathematical Sciences: L-Functions of Number Fields and Automorphic Forms

数学科学：数域的 L 函数和自守形式

• 批准号: 9500797
• 负责人: Henryk Iwaniec
• 金额: $ 21.9万
• 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: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1998-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500797&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Functions; Number; Fields

This project involves studies on two topics: 1) multiplicity of discriminants, class numbers and Artin L-functions, and 2) distribution of Hecke eigenvalues. In the first category, the main objective is to establish estimates for class group character sums which are relatively short with respect to the discriminant. On the second topic, the aim is to investigate the orthogonality and equidistribution of eigenvalues of Hecke operators. This research falls into the general area of number theory. Number theory has its historical roots in the study of the whole numbers, addressing such questions as those dealing with the divisibility of one whole number by another. It is among the oldest branches of mathematics and was pursued for many centuries for purely aesthetic reasons. However, within the last half century it has become an indispensable tool in diverse applications in areas such as data transmission and processing, and communication systems.

本课题主要研究两个主题：1)判别函数、类数和Artin l -函数的多重性；2)Hecke特征值的分布。在第一类中，主要目标是建立相对于判别的相对较短的类群特征和的估计。在第二个主题上，目的是研究Hecke算子的特征值的正交性和等分布性。这项研究属于数论的一般领域。数论的历史根源在于对整数的研究，解决的问题是一个整数能被另一个整数整除的问题。它是数学中最古老的分支之一，人们为了纯粹的美学原因而追求了许多世纪。然而，在过去的半个世纪里，它已经成为数据传输和处理以及通信系统等各种应用领域不可或缺的工具。