3 problems

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…

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