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Harmonic Weak Siegel–Maaß Forms I: Preimages of Non-Holomorphic Saito-Kurokawa Lifts

Journal article
Authors Martin Westerholt-Raum
Published in International mathematics research notices
Issue 5
Pages 1442–1472
ISSN 1073-7928
Publication year 2018
Published at Department of Mathematical Sciences
Pages 1442–1472
Language en
Links https://doi.org/10.1093/imrn/rnw288
Subject categories Other Mathematics, Geometry, Subatomic Physics

Abstract

Given a non-holomorphic Saito-Kurokawa lift we construct a preimage under the vector-valued lowering operator. In analogy with the case of harmonic weak elliptic Maaß forms, this preimage allows for a natural decomposition into a meromorphic and a non-holomorphic part. In this way every harmonic weak Siegel–Maaß form gives rise to a Siegel mock modular form.

Page Manager: Webmaster|Last update: 9/11/2012
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