Abstract
For a function ϕ(y) = o(y −1/s), y → ∞, we prove the existence of vectors ᾱ∈ℝs admitting, for any ε > 0, infinitely many simultaneous ϕ(1 + ε-approximations, but not admitting any simultaneous ϕ-approximations.
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Translated from Matematicheskie Zametki, vol. 80, no. 3, 2006, pp. 328–338.
Original Russian Text Copyright © 2006 by R. K. Akhundzhanov, N. G. Moshchevitin.
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Akhundzhanov, R.K., Moshchevitin, N.G. Vectors of given diophantine type. Math Notes 80, 318–328 (2006). https://doi.org/10.1007/s11006-006-0143-2
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DOI: https://doi.org/10.1007/s11006-006-0143-2