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Failures of the Integral Hasse Principle for Affine Quadric Surfaces

Number Theory 2025-11-25 v2

Abstract

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 work explores the frequency that such counter-examples arise in a family of affine quadric surfaces defined over the integers.

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Cite

@article{arxiv.1604.08510,
  title  = {Failures of the Integral Hasse Principle for Affine Quadric Surfaces},
  author = {Vladimir Mitankin},
  journal= {arXiv preprint arXiv:1604.08510},
  year   = {2025}
}

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20 pages