The Density of Rational Points on a Certain Threefold

Conference paper
Part of the Springer Proceedings in Mathematics book series (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 2 × 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.

Notes

Acknowledgements

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

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität GöttingenGöttingenGermany

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