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A p-ADIC HERMITIAN MAASS LIFT

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  17 April 2018

TOBIAS BERGER  and
KRZYSZTOF KLOSIN
TOBIAS BERGER
Affiliation:
School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, UK e-mail: [email protected]
KRZYSZTOF KLOSIN
Affiliation:
Department of Mathematics, Queens College CUNY, 65-30 Kissena Blvd, Queens, NY 11367, USA e-mail: [email protected]
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Abstract

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For K, an imaginary quadratic field with discriminant −DK, and associated quadratic Galois character χK, Kojima, Gritsenko and Krieg studied a Hermitian Maass lift of elliptic modular cusp forms of level DK and nebentypus χK via Hermitian Jacobi forms to Hermitian modular forms of level one for the unitary group U(2, 2) split over K. We generalize this (under certain conditions on K and p) to the case of p-oldforms of level pDK and character χK. To do this, we define an appropriate Hermitian Maass space for general level and prove that it is isomorphic to the space of special Hermitian Jacobi forms. We then show how to adapt this construction to lift a Hida family of modular forms to a p-adic analytic family of automorphic forms in the Maass space of level p.

MSC classification

Primary: 11F33: Congruences for modular and $p$-adic modular forms
Secondary: 11F50: Jacobi forms 11F55: Other groups and their modular and automorphic forms (several variables)
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 61 , Issue 1 , January 2019 , pp. 85 - 114
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

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