3 problems

Let $p$ be prime and let $U$ be a set of $p^2$ points in the affine space ${\rm AG}(3,p)$. Strong cylinder conjecture. If every plane meets $U$ in a number of points divisible by…

Let $p$ be prime, let $U$ be a set of $p^2$ points in the affine space ${\rm AG}(3,p)$, and let $N$ be the set of directions not determined by pairs of points of $U$. The cylinder…

Let $p$ be prime, let $f:{\rm GF}(p)\to{\rm GF}(p)$, and let $I(f)$ denote the minimum defined by … Let $\epsilon$ and $t$ be as in the stated hypothesis. The algebraic-curve conje…