On certain Fourier coefficients of Eisenstein series on $G_2$

Wei Xiong

Vol. 289 (2017), No. 1, 235–255

DOI: 10.2140/pjm.2017.289.235

Abstract

We compute certain Fourier coefficients of Eisenstein series on the split simple exceptional group $G_2$, and the result is a product of zeta functions and a finite product of local integrals. The method is via exceptional theta correspondence for $G_2\times {PGL}_3$.

Keywords

exceptional group, Eisenstein series, Fourier coefficients, minimal representations, exceptional theta correspondence, higher-dimensional Hensel's lemma

Mathematical Subject Classification 2010

Primary: 11F27, 11F30

Milestones

Received: 31 May 2016

Revised: 19 December 2016

Accepted: 5 February 2017

Published: 12 May 2017