no. 1
A uniform estimate for the density of rational points on quadrics
Comtat, Félicien1
1 France House Queen Mary University of London E14QA London, United Kingdom
Journal de théorie des nombres de Bordeaux, Tome 31 (2019) no. 1, pp. 243-253.

L’objet de cet article est la densité des points rationnels de hauteur bornée sur une variété définie par une forme quadratique Q à coefficients entiers. Dans le cas de quatre variables, nous donnons une estimation qui ne dépend pas des coefficients de Q. Pour davantage de variables, une estimation similaire reste vérifiée en se restreignant à ne compter que les points qui ne sont contenus dans aucune ligne rationnelle.

This paper is concerned with the density of rational points of bounded height lying on a variety defined by an integral quadratic form Q. In the case of four variables, we give an estimate that does not depend on the coefficients of Q. For more variables, a similar estimate still holds with the restriction that we only count points which do not lie on ℚ-lines.

Reçu le :
Révisé le :
Accepté le :
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DOI : 10.5802/jtnb.1078
Classification : 11D45, 11D09, 11E12
Mots clés : Uniform asymptotic estimates, quadratic forms
Comtat, Félicien 1

1 France House Queen Mary University of London E14QA London, United Kingdom 
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Comtat, Félicien. A uniform estimate for the density of rational points on quadrics. Journal de théorie des nombres de Bordeaux, Tome 31 (2019) no. 1, pp. 243-253. doi : 10.5802/jtnb.1078. http://archive.numdam.org/articles/10.5802/jtnb.1078/

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