9 problems

Let $n\in\mathbb{N}$ and let the Veronese curve be … A manifold ${\cal M}\subset\mathbb{R}^n$ is extremal if $|{\cal M}\cap{\cal S}_n(v)|_{\cal M}=0$ for every $v>1/n$. Mahler's co…

Baker's conjecture. The Veronese curve $\mathcal{V}_n$ is of Groshev type for convergence.

Baker's conjecture. In the assertion that almost all points on $C_n$ are not $psi$-approximable, Baker's condition could be replaced by the standard convergence condition. This con…

Let $\mathbf{M}_{n,1}$ be the set of nondegenerate curves in $\mathbb{R}^n$; that is, curves $\mathcal{C}=\{\mathbf{f}(x): x\in I,\ \mathbf{f}:I\to \mathbb{R}^n\}$ such that they a…

Unconditional $\gamma_n$-bound conjecture. The uniform exponent of approximation satisfies

Let $k\geq 1$ be an integer. For a real number $\zeta$, write … and consider the exponent $\chi_k$ restricted to points on the Veronese curve. Spectrum conjecture. The spectrum of…

Let $d\geq 1$ and let … be the Veronese curve. Write $\mathrm{A}(\psi_c,M,\mathbb{Q}^d,H)$ for the set of points on $M$ admitting approximation at rate $\psi_c$, let…

Let $\psi:\mathbb{N}\to\mathbb{R}^+$ be decreasing, let…

Let $n\geq 1$ and consider the Veronese curve $\{(x,\dots,x^n):x\in\mathbb{R}\}\subset\mathbb{R}^n$. A point $Y$ is very well multiplicatively approximable (VWMA) if there exists…