A Quadratic Vinogradov Mean Value Theorem in Finite Fields

Samuel Mansfield, Akshat Mudgal

Let $p$ be a prime, let $s\ge 3$ be a natural number and let $A\subseteq {\mathbb{F}}_p$ be a non-empty set satisfying $|A|\ll p^{1/2}$. Denoting $J_s(A)$ to be the number of sol…