3 problems

Let $d$ be an even integer and let $q\equiv 1\pmod{d}$. For the Dwork hypersurface … over $\mathbb{F}_q$, let $\#D^d_\lambda(\mathbb{F}_q)$ denote its number of projective…

Even-dimensional Dwork point count conjecture. The number of points over $\mathbb F_q$ on the Dwork hypersurface can be expressed as

Let $d$ be an odd prime, let $p$ be a prime such that $p\not\equiv 1 \pmod{d}$, and let … be the Dwork hypersurface over $\mathbb{F}_p$. Write…