2024/01/10 by Shunsuke Usuki, Usuki, Shunsuke
Mathematics · #Advanced Topology and Set Theory #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2401.05027
In this paper, we improve the results in the author's previous paper \citeUsu22, which deals with the quantitative problem on Littlewood's conjecture. We show that, for any 0<γ<1, any (α,β)∈ℝ2 except on a set with Hausdorff dimension about √γ, any small 0<ε<1 and any large N∈ℕ, the number of integers n∈[1,N] such that n⟨ nα⟩⟨ nβ⟩<ε is greater than γ(log N)2/(loglog N)2 up to a universal constant.