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math.DG2014
Bolza quaternion order and asymptotics of systoles along congruence subgroups
Karin Katz, Mikhail Katz, Michael Schein +1
We give a detailed description of the arithmetic Fuchsian group of the Bolza surface and the associated quaternion order. This description enables us to show that the corresponding…
math.DG2005★ 5 cited
Logarithmic growth of systole of arithmetic Riemann surfaces along congruence subgroups
Mikhail G. Katz, Mary Schaps, Uzi Vishne
We apply a study of orders in quaternion algebras, to the differential geometry of Riemann surfaces. The least length of a closed geodesic on a hyperbolic surface is called its sys…