Automorphic products of singular weight

作者：Scheithauer Nils R^*

来源：Compositio Mathematica, 2017, 153(9): 1855-1892.

DOI：10.1112/S0010437X17007266

• automorphic forms on orthogonal groups
• singular theta correspondence
• modular forms
• generalised Kac Moody algebras

We prove some new structure results for automorphic products of singular weight. First, we give a simple characterisation of the Borcherds 1)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.

• 出版日期2017-9