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Theta Series of Lattices Associated with Hyperbolic Tilings

to my knowledge (more bibliographic details shortly) none of the theta series below occur in the On-Line encyclopedia of integer sequences, and "complex hyperbolic lattices" and "lorenzian lattices" appear to be different beasties.

Bounty: I am offering a bottle of whisky to anyone who can successfully translate Jacob Lurie's Higher Topos Theory (and/or the stacks project) into the analytic combinatorical language of the manner of Flajolet's Analytic Combinatorics.