  Let $k$ be a finite field extension of the function field $\bfF_p(T)$ and
$\bar{k}$ its algebraic closure. We count points in projective space $\Bbb P
^{n-1}(\bar{k})$ with given height and of fixed degree $d$ over the field $k$.
If $n>2d+3$ we derive an asymptotic estimate for their number as the height
tends to infinity. As an application we also deduce asymptotic estimates for
certain decomposable forms.

Number Theory