Automorphic products of singular weight. (20th June 2017) - Scheithauer, Nils R.
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.