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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

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