Lambdaadic Waldspurger Packets
Lambdaadic Waldspurger Packets

Vinayak Vatsal , University of British Columbia
Fine Hall 214
Wadspurger has shown that the genuine automorphic cuspidal representations of the metaplectic cover S of SL_2 are divided naturally into packets, and that thse packets are indexed by the cuspidal automorphic representations of PGL_2. We construct packets of Lambdaadic modular forms of half integral weight, indexed by Lambdaadic forms on PGL_2. The elements of the Lambdaadic packets are nonzero, but they have specializations that vanish, owing to a trivial zero phenomenon and the sign of a complex root number. This is in contrast to the usual trivial zero phenomenon which arises from the vanishing of a padic factor.