Mathematical Notes

, Volume 80, Issue 3–4, pp 318–328 | Cite as

Vectors of given diophantine type

  • R. K. Akhundzhanov
  • N. G. Moshchevitin


For a function ϕ(y) = o(y −1/s ), y → ∞, we prove the existence of vectors ᾱ∈ℝ s admitting, for any ε > 0, infinitely many simultaneous ϕ(1 + ε-approximations, but not admitting any simultaneous ϕ-approximations.

Key words

vector of Diophantine type simultaneous Diophantine approximations Euclidean space simultaneous ϕ-approximation 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • R. K. Akhundzhanov
    • 1
  • N. G. Moshchevitin
    • 1
  1. 1.M. V. Lomonosov Moscow State UniversityMoscow

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