Geodesic
Asymptotic Formulae for Pairs of Diagonal Cubic Equations
Canadian journal of mathematics, Tome 63 (2011) no. 1, pp. 38-54

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DOI

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.
DOI : 10.4153/CJM-2010-067-3
Mots-clés : 11D72, 11P55, exponential sums, Diophantine equations 
Brüdern, Jörg; Wooley, Trevor D. Asymptotic Formulae for Pairs of Diagonal Cubic Equations. Canadian journal of mathematics, Tome 63 (2011) no. 1, pp. 38-54. doi: 10.4153/CJM-2010-067-3
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     title = {Asymptotic {Formulae} for {Pairs} of {Diagonal} {Cubic} {Equations}},
     journal = {Canadian journal of mathematics},
     pages = {38--54},
     year = {2011},
     volume = {63},
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     doi = {10.4153/CJM-2010-067-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-067-3/}
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