On Manin's conjecture for a certain singular cubic surface
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 40 (2007) no. 1, pp. 1-50. 
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     author = {de La Bret\`eche, R\'egis and Browning, Tim D. and Derenthal, Ulrich},
     title = {On {Manin's} conjecture for a certain singular cubic surface},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {1--50},
     publisher = {Elsevier},
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     year = {2007},
     doi = {10.1016/j.ansens.2006.12.002},
     zbl = {1125.14008},
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     url = {http://archive.numdam.org/articles/10.1016/j.ansens.2006.12.002/}
}
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de La Bretèche, Régis; Browning, Tim D.; Derenthal, Ulrich. On Manin's conjecture for a certain singular cubic surface. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 40 (2007) no. 1, pp. 1-50. doi : 10.1016/j.ansens.2006.12.002. http://archive.numdam.org/articles/10.1016/j.ansens.2006.12.002/

[1] Batyrev V.V., Tschinkel Y., Tamagawa numbers of polarized algebraic varieties, Astérisque 251 (1998) 299-340. | Numdam | MR | Zbl

[2] De La Bretèche R., Sur le nombre de points de hauteur bornée d'une certaine surface cubique singulière, Astérisque 251 (1998) 51-77. | Numdam | Zbl

[3] de la Bretèche R., Browning T.D., On Manin's conjecture for singular del Pezzo surfaces of degree four, I, Michigan Math. J., in press. | Zbl

[4] de la Bretèche R., Browning T.D., On Manin's conjecture for singular del Pezzo surfaces of degree four, II, Math. Proc. Camb. Phil. Soc., in press. | Zbl

[5] Browning T.D., The density of rational points on a certain singular cubic surface, J. Number Theory 119 (2006) 242-283. | MR | Zbl

[6] Bruce J.W., Wall C.T.C., On the classification of cubic surfaces, J. London Math. Soc. 19 (1979) 245-256. | MR | Zbl

[7] Chambert-Loir A., Tschinkel Y., On the distribution of points of bounded height on equivariant compactifications of vector groups, Invent. Math. 148 (2002) 421-452. | MR | Zbl

[8] Derenthal U., Manin's conjecture for a certain singular cubic surface, math.NT/0504016.

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

[10] Hassett B., Tschinkel Y., Universal torsors and Cox rings, in: Arithmetic of Higher-Dimensional Algebraic Varieties, Palo Alto, CA, 2002, Progr. Math., vol. 226, Birkhäuser, Basel, 2004, pp. 149-173. | MR | Zbl

[11] Heath-Brown D.R., The density of rational points on cubic surfaces, Acta Arith. 79 (1997) 17-30. | MR | Zbl

[12] Heath-Brown D.R., The density of rational points on Cayley's cubic surface, in: Proceedings of the Session in Analytic Number Theory and Diophantine Equations, Bonner Math. Schriften, vol. 360, Univ. Bonn, Bonn, 2003. | MR | Zbl

[13] Ivić A., The Riemann Zeta-Function, John Wiley & Sons Inc., New York, 1985. | MR | Zbl

[14] Loxton J.H., Vaughan R.C., The estimation of complete exponential sums, Canad. Math. Bull. 28 (1985) 440-454. | MR | Zbl

[15] Peyre E., Hauteurs et nombres de Tamagawa sur les variétés de Fano, Duke Math. J. 79 (1995) 101-218. | MR | Zbl

[16] Salberger P., Tamagawa measures on universal torsors and points of bounded height on Fano varieties, Astérisque 251 (1998) 91-258. | Numdam | MR | Zbl

[17] Tenenbaum G., Introduction to Analytic and Probabilistic Number Theory, translated from the second French ed., Cambridge Studies in Advanced Mathematics, vol. 46, Cambridge Univ. Press, Cambridge, UK, 1995. | MR | Zbl

[18] Titchmarsh E.C., The Theory of the Riemann Zeta-Function, second ed., revised by D.R. Heath-Brown, Oxford Univ. Press, Oxford, UK, 1986. | MR | Zbl

[19] Vaaler J.D., Some extremal functions in Fourier analysis, Bull. Amer. Math. Soc. 12 (1985) 183-216. | MR | Zbl

[20] Vaughan R.C., The Hardy-Littlewood Method, Cambridge Tracts in Mathematics, vol. 125, second ed., Cambridge Univ. Press, Cambridge, UK, 1997. | Zbl

[21] Weil A., Sur les courbes algébriques et les variétés qui s'en déduisent, Pub. Inst. Math. Strasbourg 7 (1948) 1-85. | MR | Zbl

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