Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-23T09:26:52.914Z Has data issue: false hasContentIssue false
  • English
  • Français

A Simple Proof of a Theorem of Landau

Published online by Cambridge University Press:  20 January 2009

E. M. Wright
E. M. Wright
Affiliation:
Department of Mathematics, University of Aberdeen.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let σk(x) be the number of integers n≤x which are the product of just k prime factors, so that

and let πk(x) be the number of such n for which all the pi are different.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 9 , Issue 2 , November 1954 , pp. 87 - 90
Copyright
Copyright © Edinburgh Mathematical Society 1954

References

REFERENCES

1.Gauss, C. F., Werke, vol. 10 (Göttingen 1917), 11.Google Scholar
2.Hadamard, J., Bull. Soc. Math, de France, 24 (1896), 199–220.CrossRefGoogle Scholar
3.Poussin, Ch. de la Vallée, Ann. Soc. Sc. Bruxelles, 20 II (1896), 183–256.Google Scholar
4.Landau, E., Bull. Soc. Math, de France, 29 (1900), 25–38;CrossRefGoogle Scholar
Handbuch der Lehre von der Verteilung der Primzahlen (Leipzig 1909) I, 205–13.Google Scholar
5.Landau, E., Oöttinger Nachrichten, Math.-phys. Kl. (1911), 361–381.Google Scholar
6.Shah, S. M., Indian Phys. Math. Journal, 4 (1933), 47–53 andGoogle Scholar
Proc. Acad. Sci. India, 4 (1935), 207–216.Google Scholar
7.Selberg, S., K. Norske Vidensk Selskab Forhandlinger, 13 (1940), 30–33 andGoogle Scholar
Skrifter Norske Vidensk—Akad, Oslo I Nat.—Naturv Kl., 1942, No. 5.Google Scholar
8.Selberg, A., Annals of Math., 50 (1949), 305–313.CrossRefGoogle Scholar