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

研究涉及以下一般性问题。 为 数上一般线性群的尖点表示 领域和任意复数，首席研究员 将考虑确定L是否- 的Hecke特征标张量表示的函数 有限阶数域在复数上求值 也会消失 与此相关的问题和应用程序， 数论中的其他问题也将被考虑。 主要研究者在以下一般领域工作： 所谓的朗兰纲领，一个将两个 不同类型的功能，目的是获得 深入的数论结果

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.