Exponents of Diophantine approximation in dimension two by Michel
نویسنده
چکیده
Let Θ = (α, β) be a point in R, with 1, α, β linearly independent over Q. We attach to Θ a quadruple Ω(Θ) of exponents which measure the quality of approximation to Θ both by rational points and by rational lines. The two “uniform” components of Ω(Θ) are related by an equation, due to Jarńık, and the four exponents satisfy two inequalities which refine Khintchine’s transference principle. Conversely, we show that for any quadruple Ω fulfilling these necessary conditions, there exists a point Θ ∈ R for which Ω(Θ) = Ω.
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