Diagonal hypersurfaces and elliptic curves over finite fields and hypergeometric functions

Sulakashna, Rupam Barman

Let $D_{\lambda }^{d,k}$ denote the family of diagonal hypersurface over a finite field ${\mathbb{F}}_q$ given by \begin{align*} D_λ^{d,k}:X_1^d+X_2^d=λdX_1^kx_2^{d-k}, \end{align*} where $d\…