The density of rational points on Cayley's cubic surface

Abstract

The Cayley cubic surface is given by the equation sum_{i=1}^4 X_i^{-1}=0. We show that the number of non-trivial primitive integer points of size at most B is of exact order B(log B)^6, as predicted by Manin's conjecture.

29 pages

Cited by in corpus (8)

• An overview of Manin's conjecture for del Pezzo surfaces
• Cox rings of cubic surfaces and Fano threefolds
• Manin's conjecture for a certain singular cubic surface
• On the saturation number for cubic surfaces
• Hilbert's 14th Problem and Cox Rings
• Errata and Addenda to Mathematical Constants
• Equations of the Cayley Surface
• The saturation number for Cayley's cubic surface