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Automorphic products of singular weight

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  20 June 2017

Nils R. Scheithauer
Nils R. Scheithauer*
Affiliation:
Fachbereich Mathematik, Technische Universität Darmstadt, Schloßgartenstraße 7, 64289 Darmstadt, Germany email [email protected]
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Abstract

We prove some new structure results for automorphic products of singular weight. First, we give a simple characterisation of the Borcherds function $\unicode[STIX]{x1D6F7}_{12}$. Second, we show that holomorphic automorphic products of singular weight on lattices of prime level exist only in small signatures and we derive an explicit bound. Finally, we give a complete classification of reflective automorphic products of singular weight on lattices of prime level.

Keywords

automorphic forms on orthogonal groupssingular theta correspondencemodular formsgeneralised Kac–Moody algebras

MSC classification

Primary: 11F03: Modular and automorphic functions 11F22: Relationship to Lie algebras and finite simple groups 11F27: Theta series; Weil representation; theta correspondences 11F55: Other groups and their modular and automorphic forms (several variables)
Type
Research Article
Information
Compositio Mathematica , Volume 153 , Issue 9 , September 2017 , pp. 1855 - 1892
Copyright
© The Author 2017 

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