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arXiv · 1408.4148

Lattices with many Borcherds products

Jan Hendrik Bruinier·Stephan Ehlen·Eberhard Freitag
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Abstract

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.

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Jan Hendrik Bruinier, Stephan Ehlen, Eberhard Freitag. 2014-08-18. Lattices with many Borcherds products. https://arxiv.org/abs/1408.4148

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