Local and global Maass relations

Ameya Pitale, Abhishek Saha, Ralf Schmidt

Research output: Contribution to journalArticle (Academic Journal)peer-review

3 Citations (Scopus)
224 Downloads (Pure)

Abstract

We characterize the irreducible, admissible, spherical representations of GSp4(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.
Original languageEnglish
Number of pages23
JournalMathematische Zeitschrift
Early online date9 Jan 2017
DOIs
Publication statusE-pub ahead of print - 9 Jan 2017

Keywords

  • math.NT

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