Counting points of fixed degree and bounded height

Details Counting points of fixed degree and bounded height Counting points of fixed degree and bounded height

2012-04-08

arxiv.org/abs/1204.1745v1

Acta Arith. 140 (2009), 145-168

Mathematics

Number Theory

Scientific paper

10.4064/aa140-2-4

We consider the set of points in projective $n$-space that generate an
extension of degree $e$ over given number field $k$, and deduce an asymptotic
formula for the number of such points of absolute height at most $X$, as $X$
tends to infinity. We deduce a similar such formula with instead of the
absolute height, a so-called adelic-Lipschitz height.

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