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December 2015 Some constructions of modular forms for the Weil representation of SL2(Z)
Nils R. Scheithauer
Nagoya Math. J. 220: 1-43 (December 2015). DOI: 10.1215/00277630-3335405

Abstract

Modular forms for the Weil representation of SL2(Z) play an important role in the theory of automorphic forms on orthogonal groups. In this paper we give some explicit constructions of these functions. As an application, we construct new examples of generalized Kac–Moody algebras whose denominator identities are holomorphic automorphic products of singular weight. They correspond naturally to the Niemeier lattices with root systems D122, E83 and to the Leech lattice.

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Nils R. Scheithauer. "Some constructions of modular forms for the Weil representation of SL2(Z)." Nagoya Math. J. 220 1 - 43, December 2015. https://doi.org/10.1215/00277630-3335405

Information

Received: 9 December 2013; Revised: 20 June 2014; Accepted: 13 August 2014; Published: December 2015
First available in Project Euclid: 1 December 2015

zbMATH: 1344.11039
MathSciNet: MR3429723
Digital Object Identifier: 10.1215/00277630-3335405

Subjects:
Primary: 11F27
Secondary: 11F22, 17B65

Rights: Copyright © 2015 Editorial Board, Nagoya Mathematical Journal

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Vol.220 • December 2015
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