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Suppose [itex]\Gamma[/itex] is a discrete subgroup of SL_{2}(R), which acts on the upper half complex plane as Mobius transformation. F is its fundamental domain. If z is a vertex of F which does not lie on the extended real line ( that is R[itex]\bigcup[/itex][itex]\infty[/itex] ) ,then must x be an elliptic point?? Many thanks!!

For example, if [itex]\Gamma[/itex] is SL_{2}(Z), then x is either e^{i[itex]\frac{2}{3}[/itex][itex]\pi[/itex]}or e^{i[itex]\frac{4}{3}[/itex][itex]\pi[/itex]}, both of them are elliptic points.

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# Vertex of Fundamental Domains & Elliptic Points

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