Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-05T04:03:57.517Z Has data issue: false hasContentIssue false

6 - Gaussian rational points on a singular cubic surface

from PART TWO - CONTRIBUTED PAPERS

Published online by Cambridge University Press:  05 May 2013

U. Derenthal
Affiliation:
Universität München
F. Janda
Affiliation:
Zürich, Switzerland
Alexei N. Skorobogatov
Affiliation:
Imperial College London
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[BEL07] G., Bhowmik, D., Essouabri, and B., Lichtin. Meromorphic continuation of multivariable Euler products. Forum Math., 19(6):1111–1139, 2007.Google Scholar
[Bre98] R. de la, Bretèche. Sur le nombre de points de hauteur bornée d'une certaine surface cubique singulière. Nombre et répartition de points de hauteur bornée (Paris, 1996), Astérisque, (251):51–77, 1998.Google Scholar
[BSD07] R. de la, Bretèche and P., Swinnerton-Dyer. Fonction zêta des hau¬teurs associée à une certaine surface cubique. Bull. Soc. Math. France, 135(1):65–92, 2007.Google Scholar
[BT98a] V. V., Batyrev and Yu., Tschinkel. Manin's conjecture for toric vari¬eties. J. Algebraic Geom., 7(1):15–53, 1998.Google Scholar
[BT98b] V. V., Batyrev and Yu., Tschinkel. Tamagawa numbers of polarized algebraic varieties. Nombre et répartition de points de hauteur bornée (Paris, 1996), Astérisque, (251):299–340, 1998. 1996).Google Scholar
[Der07] U., Derenthal. On a constant arising in Manin's conjecture for del Pezzo surfaces. Math. Res. Lett., 14(3):481–489, 2007.Google Scholar
[DJT08] U., Derenthal, M., Joyce, and Z., Teitler. The nef cone volume of generalized del Pezzo surfaces. Algebra Number Theory, 2(2):157–182, 2008.Google Scholar
[DP80] M., Demazure and H. C., Pinkham, editors. Séminaire sur les Singularités des Surfaces, volume 777 of Lecture Notes in Mathematics. Springer, Berlin, 1980. Held at the Centre de Mathématiques de l'École Polytechnique, Palaiseau, 1976-1977.
[DT07] U., Derenthal and Yu., Tschinkel. Universal torsors over del Pezzo surfaces and rational points. In Equidistribution in number the¬ory, an introduction, volume 237 of NATO Sci. Ser. II Math. Phys. Chem., pages 169–196. Springer, Dordrecht, 2007.
[FMT89] J., Franke, Yu. I., Manin, and Yu., Tschinkel. Rational points of bounded height on Fano varieties. Invent. Math., 95(2):421–435, 1989.Google Scholar
[Fou98] É., Fouvry. Sur la hauteur des points d'une certaine surface cubique singulière. Nombre et répartition de points de hauteur bornée (Paris, 1996), Astérisque, (251):31–49, 1998.Google Scholar
[Fre12] C., Frei. Counting rational points over number fields on a singular cubic surface, to appear in Algebra Number Theory. arXiv:1204.0383
[HBM99] D. R., Heath-Brown and B. Z., Moroz. The density of rational points on the cubic surface. Math. Proc. Cambridge Philos. Soc., 125(3):385–395, 1999.
[Lou10] D., Loughran. Manin's conjecture for a singular sextic del Pezzo surface. J. Théor. Nombres Bordeaux, 22(3):675–701, 2010.
[Pey95] E., Peyre. Hauteurs et mesures de Tamagawa sur les variétés de Fano. Duke Math. J., 79(1):101–218, 1995.Google Scholar
[Sal98] P., Salberger. Tamagawa measures on universal torsors and points of bounded height on Fano varieties. Nombre et répartition de points de hauteur bornée (Paris, 1996), Astérisque, (251):91–258, 1998.Google Scholar
[Sch64] S., Schanuel. On heights in number fields. Bull. Amer. Math. Soc., 70:262–263, 1964.Google Scholar
[Sch79] S., Schanuel. Heights in number fields. Bull. Soc. Math. France, 107(4):433–449, 1979.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×