Portal de Periódicos da CAPES

Lattices with many Borcherds products

2015; American Mathematical Society; Volume: 85; Issue: 300 Linguagem: Inglês

10.1090/mcom/3059

1088-6842

Jan Hendrik Bruinier, Stephan Ehlen, Eberhard Freitag,

Algebraic structures and combinatorial models

We prove that there are only finitely many isometry classes of even lattices $L$ of signature $(2,n)$ for which the space of cusp forms of weight $1+n/2$ for the Weil representation of the discriminant group of $L$ is trivial. We compute the list of these lattices. They have the property that every Heegner divisor for the orthogonal group of $L$ can be realized as the divisor of a Borcherds product. We obtain similar classification results in greater generality for finite quadratic modules.