N. Moshchevitin

most citedBadly approximable numbers related to the Littlewood conjecture

2 citations · 3 across the 3 of their papers we have counts for

collaborators

Showing math.NTShow all

3 papers · 1 filter

math.NT2008★ 2 cited

Badly approximable numbers related to the Littlewood conjecture

Nikolay Moshchevitin

By means of Peres-Schlag's method we prove the existence of real numbers $α, β$ such that $$ \liminf_{q\to \infty} (q\log^2 q)||αq|| ||βq|| > 0.

math.NT2007★ 1 cited

Towards BAD conjecture

Nikolay G. Moshchevitin

For $α, β, δ \in [0, 1], α + β = 1$ we consider sets $$ {\rm BAD}^* (α, β;δ) = \left\{ξ= (ξ_1,ξ_2) \in [0,1]^2: ,\inf_{p\in \mathbb{N}} \max \{(p\log(p+1))^α||pξ_1||, (p\log (p+1))^β||…

math.NT2007

On small fractional parts of polynomials

Nikolay G. Moshchevitin

We prove that for any real polynomial $f (x) \in R [x]$ the set ${α \in R : n \to \infty lim inf n lo g n ∣∣ α f (n) ∣∣ > 0}$ has positive Hausdorff dimension. Here…