仿射二次曲面上的积分点

IF 0.3 4区数学 Q4 MATHEMATICS

Journal De Theorie Des Nombres De Bordeaux Pub Date : 2020-10-22 DOI:10.5802/jtnb.1196

Tim Santens

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引用次数: 3

摘要

众所周知，Hasse原理适用于二次超曲面。对于2维光滑二次超曲面上的积分点，Hasse原理失效，但这种失效可以用Brauer-Manin障碍完全解释。我们研究了二次超曲面$ax^2 + by^2 +cz^2 = n$具有Brauer-Manin阻塞的频率。我们改进了先前的Mitankin边界。

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Integral points on affine quadric surfaces

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.

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来源期刊

Journal De Theorie Des Nombres De Bordeaux MATHEMATICS-

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： The Journal de Théorie des Nombres de Bordeaux publishes original papers on number theory and related topics (not published elsewhere).