Oscillation of the measure of irrationality function in the multidimensional case

Abstract

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 ψΘ − ψΘ' oscillates an infinite number of times as t → +∞.