Integral points on affine quadric surfaces

Abstract

It is well-known that the Hasse principle holds for quadric hypersurfaces. The Hasse principle fails for integral points on smooth quadric hypersurfaces of dimension 2 but the failure can be completely explained by the Brauer-Manin obstruction. We investigate how often the family of quadric hypersurfaces $a{x}^2+b{y}^2+c{z}^2=n$ has a Brauer-Manin obstruction. We improve previous bounds of Mitankin.

References in corpus (1)

• Failures of the Integral Hasse Principle for Affine Quadric Surfaces

Cited by in corpus (1)

• Local-global principles for semi-integral points on Markoff orbifold pairs