Inhomogeneous approximation by coprime integers
نویسندگان
چکیده
This paper addresses a problem recently raised by Laurent and Nogueira about inhomogeneous Diophantine approximation with coprime integers. A corollary of our main theorem is that for any irrational α ∈ R and for any γ ∈ R and > 0 there are infinitely many pairs of coprime integers m,n such that |nα−m− γ| ≤ 1/|n| . This improves upon previously known results, in which the exponent of approximation was at best 1/2.
منابع مشابه
Inhomogeneous approximation with coprime integers and lattice orbits
Let (ξ, y) be a point in R 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.
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