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On the number of rational points on a class of singular hypersurfaces

Abstract

Let \({\mathcal {S}}_4^m\) be a class of singular hypersurfaces defined by

$$\begin{aligned} x^{m+2}= (y_1^2+y_2^2+y_3^2+y_4^2)z^m, \end{aligned}$$

where \(m\geqslant 2\) is an integer. We establish a more precise asymptotic formula for the number of rational points of bounded height on \({\mathcal {S}}_4^m\) with a power saving error term.

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Acknowledgements

The author would like to thank her supervisor Professor Jianya Liu and host supervisor Professor Jie Wu for their help and guidance, and she is also grateful for the support of China Scholarship Council.

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China Scholarship Council.

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There is only one author, and she completed the whole work.

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Correspondence to Tingting Wen.

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Wen, T. On the number of rational points on a class of singular hypersurfaces. Period Math Hung (2022). https://doi.org/10.1007/s10998-022-00495-1

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  • DOI: https://doi.org/10.1007/s10998-022-00495-1

Keywords

  • Rational points
  • Singular hypersurface
  • Asymptotic formula
  • Power saving error term

Mathematics Subject Classification

  • 35A01
  • 65L10
  • 65L12
  • 65L20
  • 65L70