Quantum Kronecker Fractions
Abstract
A few years ago Morier-Genoud and Ovsienko introduced an interesting quantization of the real numbers as certain power series in a quantization parameter q. It is known now that the golden ratio has minimal radius among all these series. We study the rational numbers having maximal radius of convergence equal to 1, which we call Kronecker fractions. We prove that the corresponding continued fraction expansions must be palindromic and describe all Kronecker fractions with prime denominators. We found several infinite families of Kronecker fractions and all Kronecker fractions with denominator less than 10000. We also comment on the irrational case and on the relation with braids, rational knots and links.
Fields of Study & Subjects
Advanced Mathematical Identities
Geometric and Algebraic Topology
Advanced Mathematical Theories and Applications
Publication details
- Journal / source
- Journal of Experimental Mathematics
- Volume
- 2
- Issue
- 1
- Pages
- 63–80
- Publication date
- 1 March 2026
- Language
- EN