# Tag Info

I have some doubts now that $$S_m := \sum_{x \in E} \chi(f_m(x)) = 0$$ whenever $(m, q-1) = 1$ in general, but nevertheless here are some calculations that might be of help in certain cases. For now let $m$ be any integer. Clearly for any $k \in E^*$, $x \mapsto kx$ is a permutation of $E$. Let $e(z) := e^{2\pi \sqrt{-1}z}$. Thus \begin{align} (p-1) S_m ...