Inhomogeneous approximation with coprime integers and lattice orbits
Résumé
– Let (ξ, y) be a point in R 2 and ψ : N → R + a function. We investigate the problem of the existence of infinitely many pairs p, q of coprime integers such that |qξ + p − y| ≤ ψ(|q|). We give both unconditional results which are valid for every real pair (ξ, y) with ξ irrational, and metrical results valid for almost all points (ξ, y). We link the subject with density exponents of lattice orbits in R 2 .
Domaines
Mathématiques [math]Origine | Fichiers produits par l'(les) auteur(s) |
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