Counting points of fixed degree and bounded height

Abstract

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.

Cited by in corpus (2)

• On number fields with nontrivial subfields
• Effective bounds on multiplicatively dependent orbits of integer polynomials modulo S-integers