The number of solutions of diagonal cubic equations over finite fields

Wenxu Ge, Weiping Li, Tianze Wang

Let ${\mathbb{F}}_q$ be a finite field of $q=p^k$ elements. For any $z\in {\mathbb{F}}_q$, let $A_n(z)$ and $B_n(z)$ denote the number of solutions of the equations $x_1^3+x_2^3+\cdots…