Geodesic
Global $L$-packets for GSp(2) and theta lifts
Documenta mathematica, Tome 6 (2001), pp. 247-314.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $F$ be a totally real number field. We define global $L$-packets for $\GSp(2)$ over $F$ which should correspond to the elliptic tempered admissible homomorphisms from the conjectural Langlands group of $F$ to the $L$-group of $\GSp(2)$ which are reducible, or irreducible and induced from a totally real quadratic extension of $F$. We prove that the elements of these global $L$-packets occur in the space of cusp forms on $\GSp(2)$ over $F$ as predicted by Arthur's conjecture. This can be regarded as the $\GSp(2)$ analogue of the dihedral case of the Langlands-Tunnell theorem. To obtain these results we prove a nonvanishing theorem for global theta lifts from the similitude group of a general four dimensional quadratic space over $F$ to $\GSp(2)$ over $F$.
Classification : 11F70, 11F27, 11R39
Keywords: $L$-packets, arthur's conjecture, $\GSp(2)$, theta lifts 
@article{DOCMA_2001__6__a10,
     author = {Roberts, Brooks},
     title = {Global $L$-packets for {GSp(2)} and theta lifts},
     journal = {Documenta mathematica},
     pages = {247--314},
     publisher = {mathdoc},
     volume = {6},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2001__6__a10/}
}
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Roberts, Brooks. Global $L$-packets for GSp(2) and theta lifts. Documenta mathematica, Tome 6 (2001), pp. 247-314. http://geodesic.mathdoc.fr/item/DOCMA_2001__6__a10/