Geodesic
Global $L$-packets for GSp(2) and theta lifts
Documenta mathematica, Tome 6 (2001), pp. 247-314
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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.
DOI : 10.4171/dm/104
Classification : 11F27, 11F70, 11R39
Mots-clés : L-packets, arthur's conjecture, \( \GSp(2) \), theta lifts 
@article{10_4171_dm_104,
     author = {Brooks Roberts},
     title = {Global $L$-packets for {GSp(2)} and theta lifts},
     journal = {Documenta mathematica},
     pages = {247--314},
     year = {2001},
     volume = {6},
     doi = {10.4171/dm/104},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/104/}
}
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Brooks Roberts. Global $L$-packets for GSp(2) and theta lifts. Documenta mathematica, Tome 6 (2001), pp. 247-314. doi: 10.4171/dm/104

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