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Sums of three cubes. (English) Zbl 0562.10022

It is shown that the number R(N) of positive integers not exceeding N which are the sum of 3 cubes satisfies \(R(N)\gg N^{8/9-\epsilon}\), improving the exponent of 47/54-\(\epsilon\) due to Davenport. In contrast to previous results, a form of the Hardy-Littlewood method is used.
Reviewer: M.M.Dodson

MSC:

11P05 Waring’s problem and variants
11P55 Applications of the Hardy-Littlewood method
11D85 Representation problems
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