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.
