Algebraic points of bounded height on the projective line - Archive ouverte HAL Access content directly
Journal Articles Journal de Théorie des Nombres de Bordeaux Year : 2014

Algebraic points of bounded height on the projective line

Points algébriques de hauteur bornée sur la droite projective

Abstract

We consider an absolute adelic height on the set of algebraic points of the projective line P-1, associate to an ample line bundle. We give an asymptotic formula for the number of algebraic points of fixed degree and of height lower than B, when B tends to infinity. The case of the standard height on P-1 has been studied by Masser and Vaaler. We generalize this result for any adelic height using a geometric point of view and one of he known cases of the Batyrev-Manin conjecture.

Keywords

Dates and versions

hal-01143234 , version 1 (17-04-2015)

Identifiers

Cite

Cécile Le Rudulier. Algebraic points of bounded height on the projective line. Journal de Théorie des Nombres de Bordeaux, 2014, 26 (3), pp.789-812. ⟨10.5802/jtnb.888⟩. ⟨hal-01143234⟩
75 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More