70 citations · 395 across the 55 of their papers we have counts for
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Towards quantized complex numbers: -deformed Gaussian integers and the Picard group
Valentin Ovsienko
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 exist…
On radius of convergence of -deformed real numbers
Ludivine Leclere, Sophie Morier-Genoud, Valentin Ovsienko +1
We study analytic properties of ``-deformed real numbers'', a notion recently introduced by two of us. A -deformed positive real number is a power series with integer coeffic…
Quantum real numbers and -deformed Conway-Coxeter friezes
Sophie Morier-Genoud, Valentin Ovsienko
We explain the notion of "-deformed real numbers" introduced in our previous work and overview their main properties. We will also introduce -deformed Conway-Coxeter friezes.
On -deformed real numbers
Sophie Morier-Genoud, Valentin Ovsienko
We associate a formal power series with integer coefficients to a positive real number, we interpret this series as a "-analogue of a real." The construction is based on the not…
Deforming the Lie algebra of vector fields on inside the Lie algebra of pseudodifferential symbols on
C. Roger, V. Ovsienko
We classify nontrivial deformations of the standard embedding of the Lie algebra $\Vect(S^1)$ of smooth vector fields on the circle, into the Lie algebra~$\PD(S^1)$ of pseudodiffer…