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Some constructions of modular forms for the Weil representation of SL2(ℤ)

Published online by Cambridge University Press:  11 January 2016

Nils R. Scheithauer
Nils R. Scheithauer*
Affiliation:
Fachbereich Mathematik, Technische Universität Darmstadt, 64289 Darmstadt, Germanyscheithauer@mathematik.tu-darmstadt.de
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Abstract

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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 and to the Leech lattice.

Keywords

Primary 11F27Secondary 11F2217B65
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 220 , December 2015 , pp. 1 - 43
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2015

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