Arithmetic triangle groups were classified in Takeuchi, Arithmetic triangle groups, J. Math. Soc. Japan Volume 29, Number 1 (1977), 91-106. The (2,3,7) case was discussed in detail in a number of ...
It is known that for each genus, only finitely many points in the moduli space of hyperbolic genus g surfaces are arithmetic. I'm wondering if an existence result is known: for which g do we have ...