Points of bounded height on projective spaces over global function fields via geometry of numbers

TL;DR

This paper presents a new proof for counting points of bounded height on projective spaces over global function fields, adapting geometry of numbers techniques originally used in number fields.

Contribution

The authors provide a novel proof of an existing result, applying geometry of numbers methods to the setting of global function fields.

Findings

New proof of point counting result over global function fields

Adaptation of geometry of numbers techniques to function fields

Enhanced understanding of height distribution in algebraic geometry

Abstract

We give a new proof of a result of DiPippo and Wan for counting points of bounded height on projective spaces over global function fields. The new proof adapts the geometry of numbers arguments used by Schanuel in the number field case.