Diophantine approximation on polynomial curves

Abstract: In a paper from 2010, Budarina, Dickinson and Levesley studied the rational approximation properties of curves parametrized by polynomials with integral coefficients in Euclidean space of arbitrary dimension. Assuming the dimension is at least three and excluding the case of linear dependence of the polynomials together with $P(X)\equiv 1$ over the rational number field, we establish proper generalizations of their main result.