A uniform estimate for the density of rational points on quadrics
Félicien Comtat
Journal de Théorie des Nombres de Bordeaux, Volume 31 (2019) no. 1, p. 243-253

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 -lines.

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.

Received : 2018-07-02
Revised : 2018-12-12
Accepted : 2018-12-22
Published online : 2019-07-29
DOI : https://doi.org/10.5802/jtnb.1078
Classification:  11D45,  11D09,  11E12
Keywords: Uniform asymptotic estimates, quadratic forms
@article{JTNB_2019__31_1_243_0,
     author = {F\'elicien Comtat},
     title = {A uniform estimate for the density of rational points on quadrics},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {31},
     number = {1},
     year = {2019},
     pages = {243-253},
     doi = {10.5802/jtnb.1078},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/item/JTNB_2019__31_1_243_0}
}
Comtat, Félicien. A uniform estimate for the density of rational points on quadrics. Journal de Théorie des Nombres de Bordeaux, Volume 31 (2019) no. 1, pp. 243-253. doi : 10.5802/jtnb.1078. jtnb.centre-mersenne.org/item/JTNB_2019__31_1_243_0/

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