Abstract
We characterize the orbits of the principal congruence subgroup $\Gamma(n)$ of $GL_2(\bbZ)$ acting by fractional linear transformations on the real line. The characterization is in terms of congruence properties $\pmod{n}$ of the numerators and denominators of the convergents of some number in a given orbit.
Citation
Cedric Troessaert . "Fractions continues et actions des groupes de congruence sur la droite réelle." Bull. Belg. Math. Soc. Simon Stevin 14 (4) 669 - 680, November 2007. https://doi.org/10.36045/bbms/1195157135
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