3 problems

Let $a_3(n)$ and $a_4(n)$ be the Fourier coefficients of newforms … whose coefficient fields are $\mathbb{Q}\left(\sqrt{2}\right)$ and $\mathbb{Q}\left(\sqrt{3}\right)$, respective…

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

Let $l$ and $q$ be odd primes such that $q\equiv 1 \pmod{l}$, and let $z\in\mathbb{F}_{q}$ with $z\neq 0,1$. For integers $1\leq m,s<l$ satisfying $m+s=l$, consider the smooth proj…