Some constructions of modular forms for the Weil representation of SL2(ℤ). (December 2015)

• Record Type: Journal Article
• Authors: Scheithauer, Nils R.
• Is Part Of: Nagoya mathematical journal. Volume 220(2015)
• Page Start: 1
• Page End: 43
• Publication Date: 2015-12
• Subjects: Primary 11F27, -- Secondary 11F22, -- 17B65; Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathematics; Wiskunde; Electronic journals; Periodicals; 510.5
• DOI: 10.1215/00277630-3335405
• Languages: English
• ISSNs: 0027-7630

Abstract

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 and to the Leech lattice.