## Nagoya Mathematical Journal

### Some constructions of modular forms for the Weil representation of $\operatorname{SL}_{2}(\mathbb{Z})$

Nils R. Scheithauer

#### Abstract

Modular forms for the Weil representation of $\operatorname{SL}_{2}(\mathbb{Z})$ 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 $D_{12}^{2}$, $E_{8}^{3}$ and to the Leech lattice.

#### Article information

Source
Nagoya Math. J., Volume 220 (2015), 1-43.

Dates
Revised: 20 June 2014
Accepted: 13 August 2014
First available in Project Euclid: 1 December 2015

https://projecteuclid.org/euclid.nmj/1448980485

Digital Object Identifier
doi:10.1215/00277630-3335405

Mathematical Reviews number (MathSciNet)
MR3429723

Zentralblatt MATH identifier
1344.11039

#### Citation

Scheithauer, Nils R. Some constructions of modular forms for the Weil representation of $\operatorname{SL}_{2}(\mathbb{Z})$. Nagoya Math. J. 220 (2015), 1--43. doi:10.1215/00277630-3335405. https://projecteuclid.org/euclid.nmj/1448980485

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