@article{ASENS_2007_4_40_1_1_0, 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}, volume = {Ser. 4, 40}, number = {1}, year = {2007}, doi = {10.1016/j.ansens.2006.12.002}, zbl = {1125.14008}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.ansens.2006.12.002/} }
TY - JOUR AU - de La Bretèche, Régis AU - Browning, Tim D. AU - Derenthal, Ulrich TI - On Manin's conjecture for a certain singular cubic surface JO - Annales scientifiques de l'École Normale Supérieure PY - 2007 SP - 1 EP - 50 VL - 40 IS - 1 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.ansens.2006.12.002/ DO - 10.1016/j.ansens.2006.12.002 LA - en ID - ASENS_2007_4_40_1_1_0 ER -
%0 Journal Article %A de La Bretèche, Régis %A Browning, Tim D. %A Derenthal, Ulrich %T On Manin's conjecture for a certain singular cubic surface %J Annales scientifiques de l'École Normale Supérieure %D 2007 %P 1-50 %V 40 %N 1 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.ansens.2006.12.002/ %R 10.1016/j.ansens.2006.12.002 %G en %F ASENS_2007_4_40_1_1_0
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] Tamagawa numbers of polarized algebraic varieties, Astérisque 251 (1998) 299-340. | MR | Zbl
, ,[2] 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] The density of rational points on a certain singular cubic surface, J. Number Theory 119 (2006) 242-283. | MR | Zbl
,[6] On the classification of cubic surfaces, J. London Math. Soc. 19 (1979) 245-256. | MR | Zbl
, ,[7] On the distribution of points of bounded height on equivariant compactifications of vector groups, Invent. Math. 148 (2002) 421-452. | MR | Zbl
, ,[8] Manin's conjecture for a certain singular cubic surface, math.NT/0504016.
,[9] Rational points of bounded height on Fano varieties, Invent. Math. 95 (1989) 421-435. | MR | Zbl
, , ,[10] 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] The density of rational points on cubic surfaces, Acta Arith. 79 (1997) 17-30. | MR | Zbl
,[12] 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] The Riemann Zeta-Function, John Wiley & Sons Inc., New York, 1985. | MR | Zbl
,[14] The estimation of complete exponential sums, Canad. Math. Bull. 28 (1985) 440-454. | MR | Zbl
, ,[15] Hauteurs et nombres de Tamagawa sur les variétés de Fano, Duke Math. J. 79 (1995) 101-218. | MR | Zbl
,[16] Tamagawa measures on universal torsors and points of bounded height on Fano varieties, Astérisque 251 (1998) 91-258. | Numdam | MR | Zbl
,[17] 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] The Theory of the Riemann Zeta-Function, second ed., revised by D.R. Heath-Brown, Oxford Univ. Press, Oxford, UK, 1986. | MR | Zbl
,[19] Some extremal functions in Fourier analysis, Bull. Amer. Math. Soc. 12 (1985) 183-216. | MR | Zbl
,[20] The Hardy-Littlewood Method, Cambridge Tracts in Mathematics, vol. 125, second ed., Cambridge Univ. Press, Cambridge, UK, 1997. | Zbl
,[21] 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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