Automorphic products of singular weight. (20th June 2017)

• Record Type: Journal Article
• Authors: Scheithauer, Nils R.
• Is Part Of: Compositio mathematica. Volume 153:Number 9(2017)
• Page Start: 1855
• Page End: 1892
• Publication Date: 2017-06-20
• Subjects: 11F03, -- 11F22, -- 11F27, -- 11F55 (primary); automorphic forms on orthogonal groups, -- singular theta correspondence, -- modular forms, -- generalised Kac–Moody algebras; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X17007266
• Languages: English
• ISSNs: 0010-437X

Abstract

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.