On Waring’s problem: Three cubes and a minicube
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AbstractWe establish that almost all natural numbers n are the sum of four cubes of positive integers, one of which is no larger than n5/36. The proof makes use of an estimate for a certain eighth moment of cubic exponential sums, restricted to minor arcs only, of independent interest.
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Philosophical Transactions of the Royal Society of London Series A Physical and Engineering Sciences
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1993 ◽
Vol 345
(1676)
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pp. 385-396
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2004 ◽
Vol 76
(3)
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pp. 303-316
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1991 ◽
Vol 109
(2)
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pp. 229-256
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2013 ◽
Vol 94
(1)
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pp. 50-105
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1969 ◽
Vol 65
(2)
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pp. 445-446
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Philosophical Transactions of the Royal Society of London Series A Physical and Engineering Sciences
◽
1993 ◽
Vol 345
(1676)
◽
pp. 327-338
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1975 ◽
Vol 77
(2)
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pp. 269-279
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