Mathematical Sciences: Nonvanishing of L-functions for GL(2)

数学科学：GL(2) 的 L 函数不为零

• 批准号: 8803498
• 负责人: David Rohrlich
• 金额: $ 11.55万
• 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: 1988
• 资助国家: 美国
• 起止时间: 1988-06-15 至 1992-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8803498&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nonvanishing; functions; GL

The research concerns the following general problem. For cuspidal representations of the general linear group over number fields and arbitrary complex numbers, the principal investigator will consider the problem of determining whether or not the L- function of the representation tensored with Hecke characters of the number field of finite order evaluated at the complex number can vanish. Questions related to this one and applications to other problems in number theory will also be considered. The Principal Investigator is working in the general area of the so-called Langland's program, a program which relates two different looking types of functions with the goal of obtaining deep number theoretic consequences.

本研究涉及以下一般性问题。对于一般线性群在数域和任意复数上的反转表示，主要研究者将考虑确定在复数处求值的有限阶数域的带有Hecke特征的表示的L-函数是否可以消失的问题。与此相关的问题以及数论中其他问题的应用也将被考虑。首席研究员正在研究所谓的Langland程序的一般领域，该程序将两种不同类型的函数联系起来，目的是获得深入的数论结果。