Counting rational points on cubic surfaces
Nombre et répartition de points de hauteur bornée, Astérisque, no. 251 (1998), pp. 13-30 
@incollection{AST_1998__251__13_0,
     author = {Heath-Brown, Roger},
     title = {Counting rational points on cubic surfaces},
     booktitle = {Nombre et r\'epartition de points de hauteur born\'ee},
     editor = {Peyre Emmanuel},
     series = {Ast\'erisque},
     pages = {13--30},
     year = {1998},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {251},
     mrnumber = {1679837},
     zbl = {0926.11046},
     language = {en},
     url = {https://www.numdam.org/item/AST_1998__251__13_0/}
}
TY  - CHAP
AU  - Heath-Brown, Roger
TI  - Counting rational points on cubic surfaces
BT  - Nombre et répartition de points de hauteur bornée
AU  - Collectif
ED  - Peyre Emmanuel
T3  - Astérisque
PY  - 1998
SP  - 13
EP  - 30
IS  - 251
PB  - Société mathématique de France
UR  - https://www.numdam.org/item/AST_1998__251__13_0/
LA  - en
ID  - AST_1998__251__13_0
ER  - 
%0 Book Section
%A Heath-Brown, Roger
%T Counting rational points on cubic surfaces
%B Nombre et répartition de points de hauteur bornée
%A Collectif
%E Peyre Emmanuel
%S Astérisque
%D 1998
%P 13-30
%N 251
%I Société mathématique de France
%U https://www.numdam.org/item/AST_1998__251__13_0/
%G en
%F AST_1998__251__13_0
Heath-Brown, Roger. Counting rational points on cubic surfaces, dans Nombre et répartition de points de hauteur bornée, Astérisque, no. 251 (1998), pp. 13-30. https://www.numdam.org/item/AST_1998__251__13_0/

[1] H. Davenport, Cubic forms in 16 variables, Proc. Roy. Soc. A, 272 (1963), 285-303. | MR | Zbl | DOI

[2] J. Franke, Yu. I. Manin, and Yu Tschinkel, Rational points of bounded height on Fano varieties, Invent. Math., 95 (1989) 421-435. | MR | Zbl | EuDML | DOI

[3] D. R. Heath-Brown, The density of rational points on cubic surfaces, Acta Arithmetica, 272 (1997) 17-30. | MR | Zbl | EuDML | DOI

[4] M. Hindry and J. H. Silverman, The canonical height and integral points on elliptic curves, Invent. Math., 93 (1988), 419-450. | MR | Zbl | EuDML | DOI

[5] C. Hooley, On nonary cubic forms, J. reine angew. Math., 386 (1988), 32-98. | MR | Zbl | EuDML

[6] B. Mazur, Modular curves and the Eisenstein ideal, Publ. Math. IHES, 47 (1977). | MR | EuDML | Zbl | Numdam | DOI

[7] J.-F Mestre, Courbes elliptiques et formules explicites, Séminaire de théorie des nombres, Paris 1981-82, 179-182 Progress in Math., 38, (Birkhäuser, Boston, Mass., 1983). | MR | Zbl | EuDML

[8] J. Pila, The density of integral and rational points on varieties, Astérisque, 228 (1995), 183-187. | MR | Zbl | Numdam

[9] W. M. Schmidt, Diophantine Approximations and Diophantine Equations, (Springer, Berlin, 1991). | MR | Zbl | DOI

[10] I. R. Shafarevich, Algebraic number fields, Proc. Internat. Cong. Math. Stockholm, 1982, 163-176. | MR

[11] H. Weyl, Algebraic theory of numbers, (Princeton Univ. Press, N.J., 1940). | MR | JFM | Zbl

[12] H. G. Zimmer, On the difference of the Weil height and the Néron height, Math. Zeit., 147 (1976), 35-51. | MR | Zbl | EuDML | DOI