Local and global Maass relations (expanded version)
Abstract
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.
Cite
@article{arxiv.1401.3597,
title = {Local and global Maass relations (expanded version)},
author = {Ameya Pitale and Abhishek Saha and Ralf Schmidt},
journal= {arXiv preprint arXiv:1401.3597},
year = {2014}
}
Comments
30 pages, minor changes. This is a slightly expanded version of the article that has been submitted by us to a journal. A preprint of the shorter version can be downloaded from the webpage of any of the authors