Constructing Simultaneous Diophantine Approximations Of Certain Cubic Numbers
For K a cubic field with only one real embedding and α, β ϵ K, we show how to construct an increasing sequence {m_n} of positive integers and a subsequence {ψ_n} such that (for some constructible constants γ₁, γ₂ > 0): max{ǁm_nαǁ,ǁm_nβǁ} < [(γ₁)/(m_n^(¹/²))] and ǁψ_nαǁ < γ₂/[ψ_n^(¹/²) log ψ...
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| Language: | en_US |
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The University of Arizona.
2014
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| Online Access: | http://hdl.handle.net/10150/338879 |