Mathematika · 2012 · 18 citations · 6 references
Natural SciencesMathematicsNumber TheorySet TheoryCombinatorial Number TheoryComputational Number TheoryNumber-theoretic AlgorithmsBadly Approximable NumbersLittlewood's ConjectureVery Well Approximable Numbers
The Littlewood conjecture states that for all (α,β)∈ℝ2. We show that with the additional factor of log q⋅log log q, the statement is false. Indeed, our main result implies that the set of (α,β) for which is of full dimension.
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Fractal Geometry: Mathematical Foundations and Applications.
K. J. Falconer · Biometrics · 1990 · 6K citations