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Local and global Maass relations
| Content Provider | Paperity |
|---|---|
| Author | Pitale, Ameya Saha, Abhishek Schmidt, Ralf |
| Abstract | We characterize the irreducible, admissible, spherical representations of \(\mathrm{GSp}_4(F)\) (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. |
| Starting Page | 1 |
| Ending Page | 23 |
| File Format | HTM / HTML |
| ISSN | 00255874 |
| DOI | 10.1007/s00209-016-1840-5 |
| Journal | Mathematische Zeitschrift |
| e-ISSN | 14321823 |
| Language | English |
| Publisher | Springer Berlin Heidelberg |
| Publisher Date | 2017-01-09 |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
