Payne, G.; Vaserstein, L. N. 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]. Reviewer: Edward L. Cohen (Ottawa) Cited in 2 Documents MSC: 11P05 Waring’s problem and variants 11T55 Arithmetic theory of polynomial rings over finite fields Keywords:easier Waring problem for cubes; polynomials Citations:Zbl 0010.10306 PDFBibTeX XMLCite \textit{G. Payne} and \textit{L. N. Vaserstein}, Ohio State Univ. Math. Res. Inst. Publ. 2, 443--454 (1992; Zbl 0799.11039)