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The Quarterly Journal of Mathematics Advance Access published online on June 10, 2008
The Quarterly Journal of Mathematics, doi:10.1093/qmath/han017
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© 2008. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

A QUADRIC WITH ARITHMETIC PAUCITY

V. Blomer{dagger}

Department of Mathematics, University of Toronto, 40 St George Street, Toronto, Ontario, Canada M5S 2E4

J. Brüdern {ddagger}

Institut für Algebra und Zahlentheorie, Universität, Stuttgart, 70511 Stuttgart, Germany

{dagger} Corresponding author. E-mail: vblomer{at}math.toronto.edu

Received 8 April 2008;
  Abstract

The quadric given by the equations xFormula+xFormula+xFormula = yFormula+yFormula+yFormula, x1+x2+x3 = y1+y2+y3 has almost all its solutions with prime coordinates on the diagonals. This is shown in quantitative form. A similar statement holds for integral solutions whose coordinates can be written as the sum of two squares.

{ddagger} E-mail: bruedern{at}mathematik.uni-stuttgart.de


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