Abstract We compute the Hausdorff dimension of the set of simultaneously -well approximable points on the Veronese curve in R^3 for 1/3 3/5. This range for was predicted in the conjecture of Beresnevich and Yang from 3. To the best of the author’s knowledge, this makes V₃ the first nondegenerate, nonplanar curve to confirm the lower bound part of this conjecture.
Dmitry Badziahin (Fri,) studied this question.