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In /Indra's Pearls/, it's mentioned one can associate automorphic forms with limit sets. Is there an explicit description of the one associated with the Apollonian gasket (up to some appropriate discrete subgroup of $SL(2,\mathbb{R})$).

the Poincaré series or an infinite product would suit my purposes

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  • $\begingroup$ a bit pessimistic from Elena Fuchs: math.ucdavis.edu/~efuchs/FuchsStrongApprox.pdf $\endgroup$ – Will Jagy May 1 '19 at 1:54
  • $\begingroup$ I get it: her dissertation was 2010, her Bulletin article was April 2013. Kontorovich article on thin orbits in the same issue. $\endgroup$ – Will Jagy May 1 '19 at 1:57

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