We demonstrate the Batyrev-Manin Conjecture for the number of points of bounded height on hypersurfaces of some toric varieties whose rank of the Picard group is 2. The method used is inspired by the one developed by Schindler for the case of hypersurfaces of biprojective spaces and by Blomer and Brüdern for some hypersurfaces of multiprojective spaces. These methods are based on the Hardy-Littlewood circle method. The constant obtained in the final asymptotic formula is the one conjectured by Peyre.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa8050-12-2015,
author = {Teddy Mignot},
title = {Points de hauteur born\'ee sur les hypersurfaces lisses des vari\'et\'es toriques},
journal = {Acta Arithmetica},
volume = {172},
year = {2016},
pages = {1-97},
zbl = {06545341},
language = {fra},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8050-12-2015}
}
Teddy Mignot. Points de hauteur bornée sur les hypersurfaces lisses des variétés toriques. Acta Arithmetica, Tome 172 (2016) pp. 1-97. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8050-12-2015/