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math.NT2023★ 1 cited
Rational approximations, multidimensional continued fractions and lattice reduction
Valerie Berthé, Karma Dajani, Charlene Kalle +3
We first survey the current state of the art concerning the dynamical properties of multidimensional continued fraction algorithms defined dynamically as piecewise fractional maps…
math.NT2022
Lochs-type theorems beyond positive entropy
Valérie Berthé, Eda Cesaratto, Pablo Rotondo +1
Lochs' theorem and its generalizations are conversion theorems that relate the number of digits determined in one expansion of a real number as a function of the number of digits g…
math.NT2018
Some constructions for the higher-dimensional three-distance theorem
Valérie Berthé, Dong Han Kim
For a given real number , let us place the fractional parts of the points on the unit circle. These points partition the unit circle into interva…