Simultaneous Diophantine approximation on the three dimensional Veronese curve

Dmitry Badziahin

We compute the Hausdorff dimension of the set of simultaneously $\hat{I}»$-well approximable points on the Veronese curve in $\RR^3$ for $1/3\le \hat{I}»\le 3/5$. This range for $\hat{I}»$ was predi…