Oscillation of the Measure of Irrationality Function in the Multidimensional Case

摘要

It is proved that, for almost all pairs of n × m matrices Θ, Θ', in the cases m = 1 and n = 2 or m ≥ 2 and n - 1, the difference between the measure of irrationality functions ψ_Θ - ψ_Θ' oscillates an infinite number of times as t → +∞.