Simultaneous Diophantine Approximation on the 3D Veronese Curve
Abstract
Abstract We compute the Hausdorff dimension of the set of simultaneously $\lambda $-well approximable points on the Veronese curve in $\mathbb{R}^{3}$ for $1/3\leqslant \lambda \leqslant 3/5$. This range for $\lambda $ was predicted in the conjecture of Beresnevich and Yang from [3]. To the best of the author’s knowledge, this makes $\mathcal{V}_{3}$ the first nondegenerate, nonplanar curve to confirm the lower bound part of this conjecture.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Analytic Number Theory Research
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- International Mathematics Research Notices
- Volume
- 2026
- Issue
- 4
- Publication date
- 23 January 2026
- Language
- EN