Martin Widmer

Counting primitive points of bounded height

Let k be a number field and K a finite extension of k. We count points of bounded height in projective space over the field K generating the extension K/k. As the height gets large we derive asymptotic estimates with a particularly good error term respecting the extension K/k. In a future paper we will use these results to get asymptotic estimates for the number of points of fixed degree over k. We also introduce the notion of an adelic Lipschitz height generalizing that of Masser and Vaaler. This will lead to further applications involving points of fixed degree on linear varieties and algebraic numbers of fixed degree satisfying certain subfield conditions.

Counting points of fixed degree and bounded height

We consider the set of points in projective

Lipschitz class, narrow class, and counting lattice points

n

On the Northcott property and other properties related to polynomial mappings

-space that generate an extension of degree

On certain infinite extensions of the rationals with Northcott property

e

Number fields without small generators

over given number field

Counting points of fixed degree and given height over function fields

k

ON NUMBER FIELDS WITH NONTRIVIAL SUBFIELDS

, and deduce an asymptotic formula for the number of such points of absolute height at most

Bounds for the ℓ‐torsion in class groups

X

Average bounds for the

, as