2 problems

Sharp Vinogradov mean value conjecture. For every $\epsilon>0$, if $|A|$ is sufficiently large, then

For integers $n\geq 2$, parameters $0\leq \beta\leq n-1$, and $s\geq 1$, let $e(t)=e^{2\pi i t}$ and integrate over $[0,1]^{n-1}\times[0,N^{-\beta}]$. Mean value conjecture for the…