论文标题
仿射二次表面的积分点
Integral points on affine quadric surfaces
论文作者
论文摘要
众所周知，Hasse原理适用于四次超曲面。 Hasse原理在平滑的二次超曲面上的积分点失败，但可以通过Brauer-Manin障碍物完全解释故障。我们调查了二次超曲面的家族$ ax^2 + by^2 + cz^2 = n $具有brauer-manin障碍物。我们改善了Mitankin的先前范围。
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 $ax^2 + by^2 +cz^2 = n$ has a Brauer-Manin obstruction. We improve previous bounds of Mitankin.
