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Asymptotic Formulae for Pairs of Diagonal Cubic Equations

Published online by Cambridge University Press:  20 November 2018

Jörg Brüdern  and
Trevor D. Wooley
Jörg Brüdern
Affiliation:
Mathematisches Institut, Georg-August Universität Göttingen, Bunsenstrasse 3-5, D-37073 Göttingen, Germany email: bruedern@uni-math.gwdg.de
Trevor D. Wooley
Affiliation:
School of Mathematics, University of Bristol, University Walk, Clifton, Bristol BS8 1TW, United Kingdom email: matdw@bristol.ac.uk
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Abstract

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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

11D7211P55exponential sumsDiophantine equations
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 63 , Issue 1 , 01 February 2011 , pp. 38 - 54
Copyright
Copyright © Canadian Mathematical Society 2011

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