zbMATH — the first resource for mathematics

Sums of three cubes. (English) Zbl 0799.11039
Goss, David (ed.) et al., The arithmetic of function fields. Proceedings of the workshop at the Ohio State University, June 17-26, 1991, Columbus, Ohio (USA). Berlin: Walter de Gruyter. Ohio State Univ. Math. Res. Inst. Publ. 2, 443-454 (1992).
The so-called easier Waring problem for cubes (i.e., allowing negative cubes) was solved by E. M. Wright [J. Lond. Math. Soc. 9, 267–272 (1934; Zbl 0010.10306)], the sum being of \(n=5\) cubes. Here the authors consider the possibility, under certain restricted conditions, that allows integers to be the sums of 3 or 4 integral cubes. The question is then discussed for polynomials with coefficients in an arbitrary field. For the number 1, infinitely many solutions exist with \(n=3\) cubes. This problem has a long history and some of the results of that history are also shown. There is a bibliography that allows one to become familiar with this type of problem.
For the entire collection see [Zbl 0771.00031].

11P05 Waring’s problem and variants
11T55 Arithmetic theory of polynomial rings over finite fields