ON RADIUS OF CONVERGENCE OF q-DEFORMED REAL NUMBERS
Résumé
We study analytic properties of "q-deformed real numbers", a notion recently introduced by two of us. A q-deformed positive real number is a power series with integer coefficients in one formal variable q. We study the radius of convergence of these power series assuming that q ∈ C. Our main conjecture, which can be viewed as a q-analogue of Hurwitz's Irrational Number Theorem, provides a lower bound for these radii, given by the radius of convergence of the q-deformed golden ratio. The conjecture is proved in several particular cases and confirmed by a number of computer experiments. For an interesting sequence of "Pell polynomials", we obtain stronger bounds.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)