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arXiv · 1106.0696

Counting points of fixed degree and given height over function fields

Jeffrey Lin Thunder·Martin Widmer
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Abstract

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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Jeffrey Lin Thunder, Martin Widmer. 2011-06-03. Counting points of fixed degree and given height over function fields. https://doi.org/10.1112/blms%2Fbds087

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