Explicit Evaluation of Certain Exponential Sums of Quadratic Functions over $\Bbb F_{p^n}$, $p$ Odd
Sandra Draper, Xiang‐dong Hou · arXiv (Cornell University) · 2007
Let $p$ be an odd prime and let $f(x)=\sum_{i=1}^ka_ix^{p^{α_i}+1}\in\Bbb F_{p^n}[x]$, where $0\le α_10$. Assuming that all such nullities are known, we find relative formulas for $S(f,mn)$ in terms of $S(f,n)$ when $ν_p(m) \le \min\{ν_p(α_i):1\le i\le k\}$, where $ν_p$ is the $p$-adic order. We also find an explicit formula for $S(f,n)$ when $ν_2(α_1)=...= ν_2(α_k)