Local and global Maass relations
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Volume
287
Pagination
655 - 677
Publisher
DOI
10.1007/s00209-016-1840-5
Journal
Mathematische Zeitschrift
Issue
ISSN
0025-5874
Metadata
Show full item recordAbstract
We characterize the irreducible, admissible, spherical representations of GSp(4,F) (where F is a p-adic field) that occur in certain CAP representations in terms of relations satisfied by their spherical vector in a special Bessel model. These local relations are analogous to the Maass relations satisfied by the Fourier coefficients of Siegel modular forms of degree 2 in the image of the Saito-Kurokawa lifting. We show how the classical Maass relations can be deduced from the local relations in a representation theoretic way, without recourse to the construction of Saito-Kurokawa lifts in terms of Fourier coefficients of half-integral weight modular forms or Jacobi forms. As an additional application of our methods, we give a new characterization of Saito-Kurokawa lifts involving a certain average of Fourier coefficients.
Authors
Pitale, A; Saha, A; Schmidt, RCollections
- Mathematics [1468]