Exponents for three-dimensional simultaneous Diophantine approximations

2010/09/06 by Moshchevitin, Nikolay
#11J13 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1009.0987

Abstract

Let Θ= (θ₁,θ₂,θ₃)∈ ℝ³. Suppose that 1,θ₁,θ₂,θ₃ are linearly independent over ℤ. For Diophantine exponents α(Θ) = sup \γ>0: \limsup_{t→ +∞} t^γψ_Θ(t) 0: \liminf_{t→ +∞} t^γψ_Θ(t)

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