The Local Jacquet-Langlands Correspondence Via Fourier Analysis

Details The Local Jacquet-Langlands Correspondence Via Fourier Analysis The Local Jacquet-Langlands Correspondence Via Fourier Analysis

2009-06-02

arxiv.org/abs/0906.0421v2

Journal de Theorie de Nombres de Bordeaux, 22, No. 2, 2010

Mathematics

Number Theory

27 pages, corrected attribution error in Introduction

Scientific paper

Let $F$ be a locally compact non-Archimedean field, and let $B/F$ be a division algebra of dimension 4. The Jacquet-Langlands correspondence provides a bijection between smooth irreducible representations of $B^\times$ of dimension $>1$ and irreducible cuspidal representations of $GL_2(F)$. We present a new construction of this bijection in which the preservation of epsilon factors is automatic.

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