sfqm
swMATH ID:  33599 
Software Authors:  Bruinier, Jan Hendrik; Ehlen, Stephan; Freitag, Eberhard 
Description:  Lattices with many Borcherds products. 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. 
Homepage:  https://arxiv.org/abs/1408.4148 
Keywords:  finite quadratic modules; even lattices; Heegner divisor; Borcherds product 
Related Software:  eisenstein_series; SageMath; KoszulDivisorOnPic14M8; Python; LMFDB; GitHub 
Referenced in:  9 Publications 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

Lattices with many Borcherds products. Zbl 1404.11042 Bruinier, Jan Hendrik; Ehlen, Stephan; Freitag, Eberhard 
2016

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top 5
Referenced by 13 Authors
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top 5
Referenced in 7 Serials
Referenced in 4 Fields
9  Number theory (11XX) 
3  Algebraic geometry (14XX) 
1  General and overarching topics; collections (00XX) 
1  Numerical analysis (65XX) 