Sums of three cubes. (English) Zbl 0562.10022

Vaughan, R. C.

Bull. Lond. Math. Soc. 17, 17-20 (1985).

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

Keywords:

sum of three cubes; representation of integers; Hardy-Littlewood method