2013/04/01 by Liangpan Li, Li, Liangpan
Mathematics · #Analytic and geometric function theory #Mathematical Approximation and Integration #Mathematical Dynamics and Fractals #math.NT #msc:11J83
paper · pdf · doi:10.48550/arxiv.1304.0488
Accepted by the Uniform Distribution Theory journal
arxiv created 2013/04/01 · arxiv updated 2013/04/03
Given a sequence of real numbers \ψ(n)\n∈ℕ with 0≤ ψ(n)<1, let W(ψ) denote the set of x∈[0,1] for which |xn-m|<ψ(n) for infinitely many coprime pairs (n,m)∈ℕ×ℤ. The purpose of this note is to show that if there exists an ε>0 such that ∑n∈ℕψ(n)1+ε⋅(φ(n))/(n)=∞, then the Lebesgue measure of W(ψ) equals 1.