Towards quantized complex numbers: $q$-deformed Gaussian integers and the Picard group
Quantum Algebra
2023-06-22 v4 Combinatorics
Abstract
This work is a first step towards a theory of "-deformed complex numbers". Assuming the invariance of the -deformation under the action of the modular group I prove the existence and uniqueness of the operator of translations by~ compatible with this action. Obtained in such a way -deformed Gaussian integers have interesting properties and are related to the Chebyshev polynomials.
Cite
@article{arxiv.2103.10800,
title = {Towards quantized complex numbers: $q$-deformed Gaussian integers and the Picard group},
author = {Valentin Ovsienko},
journal= {arXiv preprint arXiv:2103.10800},
year = {2023}
}
Comments
21 pages