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The Density of Rational Points on a Certain Threefold

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Contributions in Analytic and Algebraic Number Theory

Part of the book series: Springer Proceedings in Mathematics ((PROM,volume 9))

Abstract

The equation

$${x}_{1}{y}_{2}{y}_{3} + {x}_{2}{y}_{1}{y}_{3} + {x}_{3}{y}_{1}{y}_{2} = 0$$

defines a singular threefold in ℙ 2 ×ℙ 2. Let N(B) be the number of rational points on this variety with non-zero coordinates of height at most B. It is proved that N(B) ≍ B(logB)4.

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References

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Acknowledgements

First author in part supported by a Volkswagen Lichtenberg Fellowship and a Starting Grant of the European Research Council.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Göttingen, Bunsenstrasse 3–5, 37073, Göttingen, Germany

    Valentin Blomer & Jörg Brüdern

Authors
  1. Valentin Blomer
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  2. Jörg Brüdern
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Correspondence to Valentin Blomer .

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Editors and Affiliations

  1. , Mathematisches Institut, Universität Göttingen, Bunsenstr. 3-5, Göttingen, 37073, Germany

    Valentin Blomer

  2. Mathematisches Institut, Universität Göttingen, Göttingen, 37073, Germany

    Preda Mihăilescu

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Blomer, V., Brüdern, J. (2012). The Density of Rational Points on a Certain Threefold. In: Blomer, V., Mihăilescu, P. (eds) Contributions in Analytic and Algebraic Number Theory. Springer Proceedings in Mathematics, vol 9. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1219-9_1

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