#### Vol. 289, No. 1, 2017

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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 ${G}_{2}×{PGL}_{3}$.

##### Keywords
exceptional group, Eisenstein series, Fourier coefficients, minimal representations, exceptional theta correspondence, higher-dimensional Hensel's lemma
##### Mathematical Subject Classification 2010
Primary: 11F27, 11F30