Journal
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY
Volume 110, Issue -, Pages 325-356Publisher
LONDON MATH SOC
DOI: 10.1112/plms/pdu054
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We obtain an essentially optimal estimate for the moment of order of the exponential sum having argument . Subject to modest local solubility hypotheses, we thereby establish that pairs of diagonal Diophantine equations, one cubic and one quadratic, possess non-trivial integral solutions whenever the number of variables exceeds 10.
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