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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].

##### MSC:
 11P05 Waring’s problem and variants 11T55 Arithmetic theory of polynomial rings over finite fields
##### Keywords:
easier Waring problem for cubes; polynomials