Points de hauteur bornée sur les hypersurfaces lisses des variétés toriques

• Autorzy: Teddy Mignot
• Języki publikacji: FR EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11D45: Counting solutions of Diophantine equations
• 11D72: Equations in many variables
• 11P55: Applications of the Hardy-Littlewood method

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2016
• Tom: 172
• Numer: 1
• Strony: 1-97

Daty

wydano

2016

Twórcy

autor

Teddy Mignot

• Institut Fourier, UMR 5582, UFR de Mathématiques, Université de Grenoble I, BP 74, 38402 Saint-Martin d'Hères Cedex, France

Identyfikatory

DOI

10.4064/aa8050-12-2015