3 problems

Restriction conjecture. If $p\le p_{d-1}=d(d-1)$, then

Let $11\le p\le 12$. Assume $a\ge b\ge 0$ and $a+b=\frac{p}{2}-3$. Let … and let $\Phi(t)=(t,t^2,t^3,t^4)$ be the moment curve in $\mathbb{R}^4$. Here $n\sim N$ denotes summation o…

For integers $n\geq 2$, real parameters $0\leq\beta\leq n-1$ and $s\geq 1$, let … and integrate over the box $[0,1]^{n-1}\times[0,N^{-\beta}]$ in the variables $x=(x_1,\ldots,x_n)$…