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Asymptotic Formulae for Pairs of Diagonal Cubic Equations

  Published:2010-08-18
 Printed: Feb 2011
  • Jörg Brüdern,
    Mathematisches Institut, Georg-August Universität Göttingen, Bunsenstrasse 3-5, D-37073 Göttingen, Germany
  • Trevor D. Wooley,
    School of Mathematics, University of Bristol, University Walk, Clifton, Bristol BS8 1TW, United Kingdom
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Abstract

We investigate the number of integral solutions possessed by a pair of diagonal cubic equations in a large box. Provided that the number of variables in the system is at least fourteen, and in addition the number of variables in any non-trivial linear combination of the underlying forms is at least eight, we obtain an asymptotic formula for the number of integral solutions consistent with the product of local densities associated with the system.
Keywords: exponential sums, Diophantine equations exponential sums, Diophantine equations
MSC Classifications: 11D72, 11P55 show english descriptions Equations in many variables [See also 11P55]
Applications of the Hardy-Littlewood method [See also 11D85]
11D72 - Equations in many variables [See also 11P55]
11P55 - Applications of the Hardy-Littlewood method [See also 11D85]
 

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