Explicit Evaluation of Certain Exponential Sums of Quadratic Functions over ${\mathbb{F}}_{p^n}$, $p$ Odd

Sandra Draper, Xiang-dong Hou

Let $p$ be an odd prime and let $f(x)={\sum }_{i=1}^k{a}_i{x}^{p^{{\alpha }_i}+1}\in {\mathbb{F}}_{p^n}[x]$, where $0\le {\alpha }_1<...<{\alpha }_k$. We consider the exponential sum $S(f,n)=\sum_{x\in\Bbb F_{p^n}}e_n(…