Counting points of fixed degree and given height over function fields

Details Counting points of fixed degree and given height over function fields Counting points of fixed degree and given height over function fields

2011-06-03

arxiv.org/abs/1106.0696v1

Mathematics

Number Theory

23 pages

Scientific paper

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.

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