2 problems

Let $\mathbb{F}$ be the finite field under consideration, let $j\in\mathbb{F}^\times$, and let $S_j$ be the sphere centered at the origin of radius $j$. Write $R_{S_j}^*(2\to r)$ f…

Let $d=2n+1$, and let … be the $d$-dimensional hyperbolic paraboloid. For a function $f:\mathbb{F}^n\times\mathbb{F}^n\to\mathbb{C}$, define … where…