The distribution of square-full integers

X. -D. Cao

doi:10.1007/bf01876369

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Periodica Mathematica Hungarica

Volume/Issue:: Volume 28: Issue 1

The distribution of square-full integers

Author:

X. -D. Cao

X. -D. Cao Beijing Petro-chemical Engineering College Daxing 102600 Beijing China

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Pages:: 43–54

Online Publication Date:: 05 Jul 2005

Publication Date:: 01 Feb 1994

Article Category:: Research Article

DOI:: https://doi.org/10.1007/bf01876369

Keywords:: Primary 11N13; Secondary 11L40; exponential sums

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Let , wheref(n) is the characteristic function of square-full integers. A formula is proved that can be used to obtain better upper bound estimate for ?(x). We get ?(x)=O(x^5/33+e), which improves the exponent 11/72 obtained by R. Blasubramania and K. Ramachandra.

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Periodica Mathematica Hungarica

Print ISSN:: 0031-5303

Online ISSN:: 1588-2829

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Periodica Mathematica Hungarica
Language	English
Size	B5
Year of Foundation	1971
Volumes per Year	2
Issues per Year	4
Founder	Bolyai János Matematikai Társulat - János Bolyai Mathematical Society
Founder's Address	H-1055 Budapest, Hungary Falk Miksa u. 12.I/4.
Publisher	Akadémiai Kiadó Springer Nature Switzerland AG
Publisher's Address	H-1117 Budapest, Hungary 1516 Budapest, PO Box 245. CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible Publisher	Chief Executive Officer, Akadémiai Kiadó
ISSN	0031-5303 (Print)
ISSN	1588-2829 (Online)