Fractions continues et équivalence sous GL - Valette, Alain (My University, 2007)
We characterize the orbits of the principal congruence subgroup Gamma(n) of GL(2)(Z) acting by fractional linear transformations on the real line. The characterization is in terms of congruence properties (mod n) of the numerators and denominators of the convergents of some number in a, given orbit.