On Manin's conjecture for a certain singular cubic surface

R. De La Bretèche, T.D. Browning, U. Derenthal, Annales Scientifiques de l’Ecole Normale Superieure 40 (2007) 1–50.

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Journal Article | Published | English
Author
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Abstract
This paper contains a proof of the Manin conjecture for the singular cubic surface S ⊂ P3 that is defined by the equation x1 x22 + x2 x02 + x33 = 0. In fact if U ⊂ S is the Zariski open subset obtained by deleting the unique line from S, and H is the usual exponential height on P3 (Q), then the height zeta function ∑x ∈ U (Q) H (x)- s is analytically continued to the half-plane R e (s) > 9 / 10.
Publishing Year
Date Published
2007-01-01
Journal Title
Annales Scientifiques de l'Ecole Normale Superieure
Acknowledgement
EPSRC grant number GR/R93155/01
Volume
40
Issue
1
Page
1 - 50
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Cite this

De La Bretèche R, Browning TD, Derenthal U. On Manin’s conjecture for a certain singular cubic surface. Annales Scientifiques de l’Ecole Normale Superieure. 2007;40(1):1-50. doi:10.1016/j.ansens.2006.12.002
De La Bretèche, R., Browning, T. D., & Derenthal, U. (2007). On Manin’s conjecture for a certain singular cubic surface. Annales Scientifiques de l’Ecole Normale Superieure, 40(1), 1–50. https://doi.org/10.1016/j.ansens.2006.12.002
De La Bretèche, Régis, Timothy D Browning, and Ulrich Derenthal. “On Manin’s Conjecture for a Certain Singular Cubic Surface.” Annales Scientifiques de l’Ecole Normale Superieure 40, no. 1 (2007): 1–50. https://doi.org/10.1016/j.ansens.2006.12.002.
R. De La Bretèche, T. D. Browning, and U. Derenthal, “On Manin’s conjecture for a certain singular cubic surface,” Annales Scientifiques de l’Ecole Normale Superieure, vol. 40, no. 1, pp. 1–50, 2007.
De La Bretèche R, Browning TD, Derenthal U. 2007. On Manin’s conjecture for a certain singular cubic surface. Annales Scientifiques de l’Ecole Normale Superieure. 40(1), 1–50.
De La Bretèche, Régis, et al. “On Manin’s Conjecture for a Certain Singular Cubic Surface.” Annales Scientifiques de l’Ecole Normale Superieure, vol. 40, no. 1, Societe Mathematique de France, 2007, pp. 1–50, doi:10.1016/j.ansens.2006.12.002.

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