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<p>We derive asymptotic formulas for the number of rational points on a smooth projective quadratic hypersurface of dimension at least three inside of a shrinking adelic open neighbourhood. This is a quantitative version of weak approximation for quadrics and allows us to deduce the best growth rate of the size of such an adelic neighbourhood for which equidistribution is preserved.</p>

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Optimal quantitative weak approximation for projective quadrics

  • 期刊论文

  • 发表日期：

    2026年2月13日

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  • Zhizhong Huang,
  • Damaris Schindler,
  • Alec Shute

摘要

We derive asymptotic formulas for the number of rational points on a smooth projective quadratic hypersurface of dimension at least three inside of a shrinking adelic open neighbourhood. This is a quantitative version of weak approximation for quadrics and allows us to deduce the best growth rate of the size of such an adelic neighbourhood for which equidistribution is preserved.