Badly approximable numbers related to the Littlewood conjecture

2008/10/04 by Nikolay Moshchevitin, Moshchevitin, Nikolay
Computer Science · Mathematics · #Advanced Topology and Set Theory #Analytic Number Theory Research #Computability, Logic, AI Algorithms #math.NT

paper · pdf · doi:10.48550/arxiv.0810.0777

5 pages

arxiv created 2008/10/04 · arxiv updated 2009/12/01

Abstract

By means of Peres-Schlag's method we prove the existence of real numbers α, β such that \liminf_{q→ ∞} (qlog² q)||αq|| ||βq|| > 0.

Related

• Badly approximable numbers and Littlewood-type problems
• Multiplicatively badly approximable numbers and generalised Cantor sets
• Metric considerations concerning the mixed Littlewood Conjecture
• An improvement of the lower bound of the number of integers in Littlewood's conjecture
• Estimating lower limit in the p-adic Littlewood conjecture