1. G. H. Hardy and J. E. Littlewood, Some problems of ?Partitio Numerorum?: I. A new solution of Waring's Problem, Göttinger Nachrichten 1920, S. 33?54: II. Proof that every large number is the sum of at most 21 biquadrates, Mathematische Zeitschrift9 (1921), S. 14?27. The third memoir of the series (Some problems of ?Partitio Numerorum?: III. On the expression of a number as a sum of primes) will appear shortly in the Acta Mathematica. The problems considered in this memoir are of a somewhat different character. We refer to these memoirs as P. N. 1, P. N. 2, P. N. 3.
2. D. Hilbert, Beweis für die Darstellbarkeit der ganzen Zahlen durch eine feste Anzahln-ter Potenzen, Göttinger Nachrichten 1909, S. 17?36: reprinted with certain changes in Mathematische Annalen,67 (1909), S. 281?300.
3. E. Landau, Zur Hardy-Littlewoodschen Lösung des Waringschen Problems, Göttinger Nachrichten 1921, S. 88?92.
4. H. Weyl, Bemerkung zur Hardy-Littlewoodschen Lösung des Waringschen Problems, Göttinger Nachrichten 1922.
5. A. Ostrowski, Bemerkung zur Hardy-Littlewoodschen Lösung des Waringschen Problems, Mathematische Zeitschrift,9 (1921), S. 28?34. We return to this point in § 6. 3.