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This work is a first step towards a theory of "q-deformed complex numbers". Assuming the invariance of the q-deformation under the action of the modular group I prove the existence and uniqueness of the operator of trans...
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We introduce a notion of q-deformed rational numbers and q-deformed continued fractions. A q-deformed rational is encoded by a triangulation of a polygon and can be computed recursively. The recursive formula is analogou...