Vol. 289, No. 1, 2017

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ISSN: 0030-8730
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 G2, and the result is a product of zeta functions and a finite product of local integrals. The method is via exceptional theta correspondence for G2 × PGL3.

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
Authors
Wei Xiong
College of Mathematics and Econometrics
Hunan University
410082 Changsha
China