Brooks Roberts

摘要

Let $F$ be a totally real number field.We define global $L$-packets for $GSp(2)$ over $F$ which shouldcorrespond to the elliptic tempered admissible homomorphisms fromthe conjectural Langlands group of $F$ to the $L$-group of $GSp(2)$ which arereducible, or irreducible and induced from a totally real quadraticextension of $F$.We prove that the elements of these global $L$-packets occur in the spaceof cusp formson $GSp(2)$ over $F$ as predicted by Arthur's conjecture. This can beregarded asthe $GSp(2)$ analogue of the dihedral case of the Langlands-Tunnelltheorem. To obtain these results we prove a nonvanishing theorem for globalthetalifts from the similitude group of a general four dimensional quadraticspace over $F$ to $GSp(2)$ over $F$.