Borcherds products of half-integral weight

Wang, Haowu; Williams, Brandon

doi:10.1016/j.jnt.2021.10.008

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Borcherds products of half-integral weight

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Wang, Haowu
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1016/j.jnt.2021.10.008
(Publisher version)

https://doi.org/10.48550/arXiv.2007.00055
(Preprint)

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Citation

Wang, H., & Williams, B. (2022). Borcherds products of half-integral weight. Journal of Number Theory, 238, 944-950. doi:10.1016/j.jnt.2021.10.008.

Cite as: https://hdl.handle.net/21.11116/0000-0009-A47A-5

Abstract

We give a necessary and sufficient criterion for the existence of Borcherds
products of half-integral weight associated to even lattices that split two
hyperbolic planes. In particular we prove that half-integral weight Borcherds
products exist for lattices of arbitrary rank.