3 problems

Let $p$ be prime, let $\chi(x)=\left(\frac{x}{p}\right)$ denote the Legendre symbol, and let $\{r_1,\ldots,r_k\}\subseteq\mathbb{Z}_p$. For distinct indices $i,j$, set $a=r_j-r_i$…

Legendre-symbol RIP conjecture. There exists a universal constant $C$ such that for every $\delta>0$, there exist $N_0>0$ and $P_0(N)=O(2^{\operatorname{poly}(N)})$ such that, when…

Optimal sampling bound conjecture. A random subset $\Omega\subset\{0,1,\ldots,n-1\}$ of average cardinality