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Article Dans Une Revue Moscow Mathematical Journal Année : 2023

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.
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Dates et versions

hal-03363862 , version 1 (04-10-2021)
hal-03363862 , version 2 (28-09-2023)

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Ludivine Leclere, Sophie Morier-Genoud, Valentin Ovsienko, Alexander Veselov. ON RADIUS OF CONVERGENCE OF q-DEFORMED REAL NUMBERS. Moscow Mathematical Journal, 2023, ⟨10.48550/arXiv.2102.00891⟩. ⟨hal-03363862v2⟩
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