Skip to main content
eScholarship
Open Access Publications from the University of California

UC Santa Cruz

UC Santa Cruz Electronic Theses and Dissertations bannerUC Santa Cruz

Schwartz spaces and local zeta integrals for powers of Hecke characters

Creative Commons 'BY-NC-ND' version 4.0 license
Abstract

We provide alternative constructions for the Local Langlands Correspondence for certain reductive groups through elementary integrals. Following the work of Matchett, Tate, Iwasawa, and Godement-Jacquet, we generate L-functions through integral representations which facilitate alternative proofs of their functional equations. We investigate, via difference operators, viable spaces as replacements for the usual Schwartz spaces, which produce L-functions which were previously not accessible through integrals. In particular, we realize the vision of Braverman-Kazhdan for the GL(1, K) case involving powers of Hecke characters.

Main Content
For improved accessibility of PDF content, download the file to your device.
Current View