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Lattices in the sense of discrete subgroups of Euclidean spaces, as used in number theory, discrete geometry, Lie groups, etc. (Not to be confused with lattice theory or lattices as used in physics! For lattices (ordered sets), use the tag: [lattice-theory])
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Modularity of certain theta series associated to hyperbolic lattice
Note that generally hyperbolic lattices will have infinitely many vectors of a given positive norm, but there should be finitely many orbits of vectors of positive norm. … Since general lattices are hard to understand, I would also be curious about results with more restrictive hypotheses, such as $L$ being unimodular i.e. $L=II_{1,k}$. …
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Modularity of certain theta series associated to hyperbolic lattice
For the purpose of someone seeing this question, I'll describe what I've figured out so far, which I think elaborates on Paul's comment. Though a warning: This isn't my forte so there may be errors. A …