Given a square-free integer d we introduce an affine hypersurface whose integer points are in one-to-one correspondence with ideal classes of the quadratic number field \(Q(\sqrt{\delta})\). Using this we relate class number problems of Gauss to Lang conjectures.
Keywords
- Subgroups of the modular group
- binary quadratic forms
- class number problems
- çark hypersurfaces
- rational points on hypersurfaces
- complex hyperbolic manifolds
- Lang conjectures
- Kobayashi hyperbolicity