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The Quarterly Journal of Mathematics Advance Access originally published online on September 2, 2007
The Quarterly Journal of Mathematics 2008 59(1):29-53; doi:10.1093/qmath/ham022
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© 2007. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

THE DENSITY OF INTEGRAL POINTS ON COMPLETE INTERSECTIONS

Oscar Marmon{dagger}

Mathematical Sciences, Chalmers University of Technology, SE-412 96 Göteborg, Sweden
Mathematical Sciences, Göteborg University, SE-412 96 Göteborg, Sweden

{dagger} E-mail: marmon{at}chalmer.se

Received 2 January 2007; revised 23 February 2007
  Abstract

In this paper, an upper bound for the number of integral points of bounded height on an affine complete intersection defined over Z is proven. The proof uses an extension to complete intersections of the method used for hypersurfaces by Heath-Brown (The density of rational points on non-singular hypersurfaces, Proc. Indian Acad. Sci. Math. Sci. 104 (1994) 13–29), the so called ‘q-analogue’ of van der Corput's AB process.


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