Local Newforms for GSp(4)

Brooks Roberts, Ralf Schmidt (auth.)354073323X, 978-3-540-73323-2

Local Newforms for GSp(4) describes a theory of new- and oldforms for representations of GSp(4) over a non-archimedean local field. This theory considers vectors fixed by the paramodular groups, and singles out certain vectors that encode canonical information, such as L-factors and epsilon-factors, through their Hecke and Atkin-Lehner eigenvalues. While there are analogies to the GL(2) case, this theory is novel and unanticipated by the existing framework of conjectures. An appendix includes extensive tables about the results and the representation theory of GSp(4).

Table of contents :
Front Matter….Pages I-VIII
A Summary….Pages 1-25
Representation Theory….Pages 27-83
Paramodular Vectors….Pages 85-122
Zeta Integrals….Pages 123-149
Non-supercuspidal Representations….Pages 151-186
Hecke Operators….Pages 187-237
Proofs of the Main Theorems….Pages 239-267
Back Matter….Pages 269-307