Hostname: page-component-848d4c4894-pftt2 Total loading time: 0 Render date: 2024-04-30T10:39:57.479Z Has data issue: false hasContentIssue false
  • English
  • Français

On square-full integers in a short interval

Published online by Cambridge University Press:  18 May 2009

P. Shiu
P. Shiu
Affiliation:
Department of Mathematics, University of Technology, Loughborough, Leicestershire, England
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.

A positive integer nis called a square-full integer if p2 divides n whenever p is a prime divisor of n. For x > 1 we denote by Q(x) the number of square-full integers not exceeding x. Bateman and Grosswald [1] proved that

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 25 , Issue 1 , January 1984 , pp. 127 - 134
Copyright
Copyright © Glasgow Mathematical Journal Trust 1984

References

REFERENCES

1.Bateman, P. T. and Grosswald, E., On a theorem of Erdos and Szekeres, Illinois J. Math. 2 (1958), 88–98.Google Scholar
2.Ivic, A. and Shiu, P., The distribution of powerful integers, Illinois J. Math. 26 (1982), 576–590.Google Scholar
3.Landau, E., Über die Anzahl der Gitterpunkte in gewissen Bereichen (II), Nachr. Ges. Wiss. Gottingen (1915), 209–243.Google Scholar
4.Phillips, E., The zeta-function of Riemann: further developments of van der Corput's method, Quart. J. Math. Oxford 41 (1933), 209–225.Google Scholar
5.Rankin, R. A., van der Corput's method and the theory of exponent pairs, Quart. J. Math. Oxford Ser. 26 (1955), 147–153.Google Scholar
6.Richert, H. E., Über die Anzahl Abelscher Gruppen gegebener Ordnung (I), Math. Z. 56 (1952), 21–32.Google Scholar
7.Roth, K. F., On the gaps between squarefree numbers, J. London Math. Soc. 26 (1951), 263–268.Google Scholar
8.Shiu, P., On the number of square-full integers between successive squares, Mathematika 27 (1980), 171–178.Google Scholar
9.Srinivasan, B. V., On the number of Abelian groups of a given order, Ada Arith. 23 (1973), 195–205.Google Scholar
10.van der Corput, J. G., Verscharfung der Abschatzung beim Teilerproblem, Math. Ann. 87 (1922), 39–65.Google Scholar