Failures of the Integral Hasse Principle for Affine Quadric Surfaces

摘要

Quadric hypersurfaces are well-known to satisfy the Hasse principle. However,this is no longer true in the case of the Hasse principle for integral points,where counter-examples are known to exist in dimension 1 and 2. This workexplores the frequency that such counter-examples arise in a family of affinequadric surfaces defined over the integers.