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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
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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

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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