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The skew-Maass lift I: The case of harmonic Maass-Jacobi forms

Journal article
Authors Martin Westerholt-Raum
O. K. Richter
Published in Research in the Mathematical Sciences
Volume 6
Issue 2
ISSN 2522-0144
Publication year 2019
Published at Department of Mathematical Sciences
Language en
Keywords Maass lift of harmonic Maass-Jacobi forms, Saito-Kurokawa lift, Kohnen limit process, Real-analytic, siegel cusp forms, rankin-selberg convolution, eisenstein-series, fourier coefficients, modular-forms
Subject categories Algebra and geometry, Geometry


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.

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