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On Waring’s problem for cubes. (English) Zbl 0021.10601

MSC:
11P05 Waring’s problem and variants
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[1] Partitio Numerorum VI,Math. Zeitschrift, 23 (1925), 1–37.
[2] Expositions of the general method (of which the proof of this Lemma is a particular case) will appear in the Proc. Royal Soc., and in Acta Arithmetica.
[3] References to Landau are toVorlesungen über Zahlentheorie, (Leipzig 1927), volume 1.
[4] An alternative method of proof is given in Landau, Satz 329 to satz 337. The less precise result obtainable by a single partial summation would in fact also suffice, but then the proof of Lemma 11 would be much more complicated.
[5] This violates the usual convention connecting the upper bound for the denominators of the major ares with the order of the Farey dissection. It corresponds, however, to the fundamentally different ways in which the arcs are treated.
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