2 problems

Let $p=2r+1$ be a Sophie Germain prime, so that $r$ is also prime, and let $\alpha\in{\mathbb{F}}_{2^r}^*$ be the Gauss period associated with $p$. Gao–Vanstone conjecture. The Gau…

Let $q$ be a power of a prime $p$, let $\gamma$ be a primitive element of ${\mathbb F}_q$, and let $N>1$ divide $q-1$. The Gauss periods $\psi(\gamma^a C_0^{(N,q)})$ for…