THE IMAGES UNDER THE MODULAR GROUP AND EXTENDED MODULAR GROUP

In this paper we obtain the image of each element of C under the modular and extended modular group by continued fractions. The modular group takes the upper half of the complex plane into itself. Using these images, unlike known methods, we can show that the extended modular group takes the upper half of the complex plane into H.

Keywords:

Modular group, Extended modular group, Continued fraction, Upper half plane 2000 AMS Classification: 20 H 10,

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