Cyclotomy of Weil Sums of Binomials

Yves Aubry, Daniel J. Katz, Philippe Langevin

The Weil sum $W_{K,d}(a)={\sum }_{x\in K}\psi (x^d+ax)$ where $K$ is a finite field, $\psi$ is an additive character of $K$, $d$ is coprime to $|K^{\times }|$, and $a\in K^{\times }$ arises…