Loughborough University
Browse
ConvergeFinal_MMJ.pdf (387.28 kB)

On radius of convergence of q-deformed real numbers

Download (387.28 kB)
journal contribution
posted on 2024-03-07, 15:14 authored by Ludivine Leclere, Sophie Morier-Genoud, Valentin Ovsienko, Alexander VeselovAlexander Veselov
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 conjecture is proved for certain class of rational numbers and confirmed by a number of computer experiments. We also prove the explicit lower bounds for the radius of convergence for the q-deformed convergents of golden and silver ratios. 

Funding

ANR project ANR-19-CE40-0021

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Moscow Mathematical Journal

Volume

24

Issue

1

Pages

1 - 19

Publisher

Independent University of Moscow, together with the Mathematical Department of the Higher School of Econonics and Moscow Center for Continuous Mathematical Education

Version

  • VoR (Version of Record)

Rights holder

© Independent University of Moscow, Mathematical Department of the Higher School of Econonics, Moscow Center for Continuous Mathematical Education

Publisher statement

Materials in this journal may be reproduced by any means for educational and scientific purposes without fee or permission (provided that the customary acknowledgment of the source is given). This consent does not extend to other kinds of copying for general distribution, for advertising or promotional purposes, or for resale.

Publication date

2024-01-01

ISSN

1609-3321

eISSN

1609-4514

Language

  • en

Depositor

Prof Alexander Veselov. Deposit date: 5 March 2024

Usage metrics

    Loughborough Publications

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC