The skew-Maass lift I: The case of harmonic Maass-Jacobi forms
Artikel i vetenskaplig tidskrift, 2019
The classical Maass lift is a map from holomorphic Jacobi forms to holomorphic scalar-valued Siegel modular forms. Automorphic representation theory predicts a non-holomorphic and vector-valued analogue for Hecke eigenforms. This paper is the first part of a series of papers. In this series of papers, we provide an explicit construction of the non-holomorphic Maass lift that is linear and also applies to non-eigenforms. In this first part, we develop new techniques to study Fourier series expansions of Siegel modular forms, which allow us to construct a Maass lift from harmonic Maass–Jacobi forms to scalar-valued Maass–Siegel forms.
Saito–Kurokawa lift
Real-analytic Siegel modular forms
Maass lift of harmonic Maass–Jacobi forms
Kohnen limit process
Maass–Siegel forms
Författare
Martin Raum
Chalmers, Matematiska vetenskaper, Algebra och geometri
Olav K. Richter
University of North Texas
Research in Mathematical Sciences
2522-0144 (ISSN) 2197-9847 (eISSN)
Vol. 6 22Siegel modulära genererande funktioner
Vetenskapsrådet (VR) (2015-04139), 2016-01-01 -- 2019-12-31.
Ämneskategorier (SSIF 2011)
Algebra och logik
Geometri
Matematisk analys
DOI
10.1007/s40687-019-0184-2