On $q$-deformed real numbers

Sophie Morier-Genoud (1) , Valentin Ovsienko (2)

1 IMJ - Institut de Mathématiques de Jussieu
2 CNRS - Centre National de la Recherche Scientifique

We associate a formal power series with integer coefficients to a positive real number, we interpret this series as a "q-analogue of a real." The construction is based on the notion of q-deformed rational number introduced in arXiv:1812.00170. Extending the construction to negative real numbers, we obtain certain Laurent series.

Domaines: Mathématiques [math]

Sophie Morier-Genoud, Valentin Ovsienko. On $q$-deformed real numbers. Experimental Mathematics, 2019, pp.1-9. ⟨10.1080/10586458.2019.1671922⟩. ⟨hal-02270544v2⟩