ON THE DISTRIBUTION OF k-TH POWER FREE INTEGERS, II

Takanobu, Satoshi; Duy, Trinh Khanh

doi:https://doi.org/10.18910/26013

このアイテムのアクセス数:65件（2022-10-04 09:59 集計）

このアイテムへのリンクには次のURLをご利用ください: https://doi.org/10.18910/26013

このアイテムへのリンクには次のURLをご利用ください: https://hdl.handle.net/11094/26013

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論文情報

タイトル	ON THE DISTRIBUTION OF k-TH POWER FREE INTEGERS, II
著者	NRID 1000040197124 1000040197124 著者名 Takanobu, Satoshi
著者	NRID 1000000726127 1000000726127 著者名 Duy, Trinh Khanh
抄録	The indicator function of the set of k-th power free integers is naturally extended to a random variable X^(k)(・) on (Z^, λ), where Z^ is the ring of finite integral adeles and λ is the Haar probability measure. In the previous paper, the first author noted the strong law of large numbers for {X^(k)(・ + n)}_n^∞, and showed the asymptotics: E^λ[(Y_N^(k))^2] ≍ 1 as N → 1, where Y_N^(k)(x) := N^(-1/2k) Σ_{n=1}^N (X^(k)(x + n) - 1/ξ(k)) . In the present paper, we prove the convergence of E^λ[(Y_N(k))^22]. For this, we present a general proposition of analytic number theory, and give a proof to this.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻	50
号	3
開始ページ	687
終了ページ	713
刊行年月	2013-09
言語	英語
ハンドルURL	https://hdl.handle.net/11094/26013
DOI	https://doi.org/10.18910/26013
ISSN	00306126
NCID	AA00765910
アクセス権	open access
出版タイプ	Version of Record
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 50, Number 3　(2013-9）

資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
DCMI資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics.50(3) p.687-p.713
DC.title	ON THE DISTRIBUTION OF k-TH POWER FREE INTEGERS, II
DC.creator	Takanobu, Satoshi
DC.creator	Duy, Trinh Khanh
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2013-09
DCTERMS.abstract	The indicator function of the set of k-th power free integers is naturally extended to a random variable X^(k)(・) on (Z^, λ), where Z^ is the ring of finite integral adeles and λ is the Haar probability measure. In the previous paper, the first author noted the strong law of large numbers for {X^(k)(・ + n)}_n^∞, and showed the asymptotics: E^λ[(Y_N^(k))^2] ≍ 1 as N → 1, where Y_N^(k)(x) := N^(-1/2k) Σ_{n=1}^N (X^(k)(x + n) - 1/ξ(k)) . In the present paper, we prove the convergence of E^λ[(Y_N(k))^22]. For this, we present a general proposition of analytic number theory, and give a proof to this.
DC.identifier	10.18910/26013
DC.format	application/pdf
citation_doi	https://doi.org/10.18910/26013
citation_title	ON THE DISTRIBUTION OF k-TH POWER FREE INTEGERS, II
citation_author	Takanobu, Satoshi
citation_author	Duy, Trinh Khanh
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2013-09
citation_journal_title	Osaka Journal of Mathematics
citation_volume	50
citation_issue	3
citation_firstpage	687
citation_lastpage	713
citation_issn	00306126
citation_public_url	https://hdl.handle.net/11094/26013
citation_doi_detail	10.18910/26013

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