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More on inhomogeneous diophantine approximation

Christopher G. Pinner — 2001

Journal de théorie des nombres de Bordeaux

For an irrational real number α and real number γ we consider the inhomogeneous approximation constant M ( α , γ ) : = lim inf | n | | n | | | n α - γ | | via the semi-regular negative continued fraction expansion of α α = 1 a 1 - 1 a 2 - 1 a 3 - and an appropriate alpha-expansion of γ . We give an upper bound on the case of worst inhomogeneous approximation, ρ ( α ) : = sup γ 𝐙 + α 𝐙 M ( α , γ ) , which is sharp when the partial quotients ai are almost all even and at least four. When the negative expansion...

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