The classic 1994
P. Buser and P. Sarnak
explores systolic ramifications of the properties of congruence
subgroups of Fuchsian groups, in the case of rational trace field.
(1996) makes tantalizing remarks in section 3.C.6.
Much arithmetic work was done by
| P. Schmutz Schaller
from 1993 until 2001.
The 2007 text
treats both the Fuchsian and the Kleinian cases, over an arbitrary
See also related work by R. Brooks (1999) on Platonic surfaces, as
well as papers by P. Sarnak and X. Xue, N. Bergeron, etc.
The general philosophy is that lower bounds for the eigenvalue of the
Laplacian should yield good systolic lower bounds asymptotically.
Brooks obtains a lower bound of 5/36 for the Platonic surfaces he
constructs by compactifying congruence surfaces of the modular group.
He did not clarify the systolic behavior of the resulting compact
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