UC Santa Cruz

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.