On Radius of Convergence of q-Deformed Real Numbers
Ludivine Leclere,
Sophie Morier-Genoud,
Valentin Ovsienko
et al.
Abstract: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 is a complex variable. Our main conjecture, which can be viewed as a q-analogue of Hurwitz's Irrational Number Theorem, claims that the q-deformed golden ratio has the smallest radius of convergence among all real numbers. The conjectur… Show more
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