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Asymptotic Formulae for Pairs of Diagonal Cubic Equations

Published online by Cambridge University Press:  20 November 2018

Jörg Brüdern
Affiliation:
Mathematisches Institut, Georg-August Universität Göttingen, Bunsenstrasse 3-5, D-37073 Göttingen, Germany email: [email protected]
Trevor D. Wooley
Affiliation:
School of Mathematics, University of Bristol, University Walk, Clifton, Bristol BS8 1TW, United Kingdom email: [email protected]
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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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2011

References

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