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# On a Conjecture of Jacquet, Lai, and Rallis: Some Exceptional Cases

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Published:2007-12-01
Printed: Dec 2007
• David Ginzburg
• Erez Lapid
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## Abstract

We prove two spectral identities. The first one relates the relative trace formula for the spherical variety $\GSpin(4,3)/G_2$ with a weighted trace formula for $\GL_2$. The second relates a spherical variety pertaining to $F_4$ to one of $\GSp(6)$. These identities are in accordance with a conjecture made by Jacquet, Lai, and Rallis, and are obtained without an appeal to a geometric comparison.
 MSC Classifications: 11F70 - Representation-theoretic methods; automorphic representations over local and global fields 11F72 - Spectral theory; Selberg trace formula 11F30 - Fourier coefficients of automorphic forms 11F67 - Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols

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