Newforms of Saito-Kurokawa lifts

Abstract

A new- and old-form theory for Bessel periods of Saito-Kurokawa representations is given. We introduce arithmetic subgroups so that a local Bessel vector fixed by the subgroup indexed by the conductor of the representation is unique up to scalars. The global Langlands L-function of a holomorphic Saito-Kurokawa representation coincides with a canonically settled Piatetski-Shapiro zeta integral of the newform.

References in corpus (2)

• Bessel models for lowest weight representations of GSp(4,R)
• Local Whittaker-Newforms for GSp(4) matching to Langlands parameters