Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-29T05:22:30.829Z Has data issue: false hasContentIssue false
  • English
  • Français

On the number of finite non-isomorphic Abelian groups in short intervals*

Published online by Cambridge University Press:  24 October 2008

Li Hongze
Li Hongze
Affiliation:
Department of Mathematics, Shandong University, Jinan, Shandong, 250100, People's Republic of China
Get access Rights & Permissions [Opens in a new window]

Extract

Let a(n) denote the number of non-isomorphic Abelian groups of order n. It is well-known that

for a natural number k we define

and

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 117 , Issue 1 , January 1995 , pp. 1 - 5
Copyright
Copyright © Cambridge Philosophical Society 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Filaseta, M. and Trifonov, O.. On gaps between square-free numbers II. J. London Math. Soc. (2) 45 (1992), 215–221.Google Scholar
[2]Halberstam, H. and Roth, K. F.. On the gaps between consecutive k-free integers. J. London Math. Soc. 26 (1951), 268–273.CrossRefGoogle Scholar
[3]Ivić, A.. On the number of finite non-isomorphic Abelian groups in short intervals. Math. Nachr. 101 (1981), 257–271.Google Scholar
[4]Ivić, A.. The Riemann Zeta-Function (Wiley, 1985).Google Scholar
[5]Krätzel, E.. Die Werteverteilung der Anzahl der nicht-isomorphen Abelschen Gruppen endlicher Ordnung in kurzen Intervallen. Math. Nachr. 98 (1980), 135–144.Google Scholar
[6]Krätzel, E.. Lattice Points (D. V. W. Berlin, 1988).Google Scholar