• Corpus ID: 232092186

The natural extension of the Gauss map and Hermite best approximations

@inproceedings{Chevallier2021TheNE,
  title={The natural extension of the Gauss map and Hermite best approximations},
  author={N. Chevallier},
  year={2021}
}
Hermite best approximation vectors of a real number θ were introduced by Lagarias. A nonzero vector (p, q) ∈ Z × N is a Hermite best approximation vector of θ if there exists ∆ > 0 such that (p − qθ) + q/∆ ≤ (a − bθ) + b/∆ for all nonzero (a, b) ∈ Z. Hermite observed that if q > 0 then the fraction p/q must be a convergent of the continued fraction expansion of θ and Lagarias pointed out that some convergents are not associated with a Hermite best approximation vectors. In this note we show… 

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