\displaystyle  \sum_{x \in ({\bf F}_{q^n}^\times)^d} \varepsilon^{\hbox{Tr}_{nr}( P(x) )} = \sum_{x \in \mu_{q^n-1}^d} G(x) G(x^q) \dots G(x^{q^{r-1}}) \ \ \ \ \ (22)