Local factors, central characters, and representations of the general linear group over non-Archimedean local fields.

摘要

he problem discussed in this thesis addresses the local version of the converse theorem for GL(n, A), the origin of which can be traced back to Tate's construction in his thesis (T), or further back to the first converse theorem proved by Hamburger (Ha1) (Ha2) (Ha3) in 1921 and 1922. We show, by using the functional equations given locally, that the representations of GL(n, F) are determined uniquely by their central characters and