Some problems of ?Partitio numerorum? (VI): Further researches in Waring's Problem-Reference-Cited by-同舟云学术

Some problems of ?Partitio numerorum? (VI): Further researches in Waring's Problem

Published:1925-12 Issue:1 Volume:23 Page:1-37
ISSN:0025-5874
Container-title:Mathematische Zeitschrift
language:en
Short-container-title:Math Z

Author:

Hardy G. H.,Littlewood J. E.

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Link

http://link.springer.com/content/pdf/10.1007/BF01506218.pdf

Reference36 articles.

1. That is to say, there is a constantA such that more thanAn numbers less thann are sums of 7 cubes. This result is due to Baer (W. S. Baer, Über die Zerlegung der ganzen Zahlen in sieben Kuben, Mathematische Annalen74 (1913), 511?514).

2. E. Landau, Über die Anzahl der Gitterpunkte in gewissen Bereichen, Göttinger Nachrichten (1912), 687?771 (750).

3. A. Hurwitz, Über die Darstellung der ganzen Zahlen als Summen vonn-ten Potenzen ganzer Zahlen, Mathematische Annalen65 (1908), 424?427.

4. See P. N. 4, 179 (Theorem 4). The ground of the inequalityG (k)??(k) being (except fork=4) the existence of a forbidden arithmetical progression, the same inequality holds forG 1 (k).

5. See P. N. 4, 179, f. n. 28) Compare P. N. 5, 52 (Lemma 10). This point aboutk=4 is overlooked on p. 188 (last sentence).

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