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Best simultaneous diophantine approximations of some cubic algebraic numbers

Nicolas Chevallier (2002)

Journal de théorie des nombres de Bordeaux

Let α be a real algebraic number of degree 3 over whose conjugates are not real. There exists an unit ζ of the ring of integer of K = ( α ) for which it is possible to describe the set of all best approximation vectors of θ = ( ζ , ζ 2 ) .’

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