Hausdorff dimension of sets of numbers whose continued fractions contain arbitrarily long arithmetic progressions.
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| Title: | Hausdorff dimension of sets of numbers whose continued fractions contain arbitrarily long arithmetic progressions. |
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| Authors: | Nakajima, Yuto1 (AUTHOR) yunakaji@mail.doshisha.ac.jp, Takahasi, Hiroki2 (AUTHOR) hiroki@math.keio.ac.jp, Wang, Baowei3 (AUTHOR) bwei_wang@hust.edu.cn |
| Source: | Journal of Number Theory. Oct2026, Vol. 287, p72-94. 23p. |
| Subjects: | Continued fractions, Arithmetic series, Irrational numbers, Mathematical sequences, Fractal dimensions, Fractals |
| Abstract: | Continued fractions with prescribed structures on sequences of their partial quotients have been intensively studied in the literature. As far as an integer sequence, especially a randomly generated one is concerned, an attractive question is whether it contains arbitrarily long arithmetic progressions. In this paper we study the fractal structure of irrational numbers whose sequences of partial quotients are strictly increasing and contain arbitrarily long, quantified arithmetic progressions. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Number Theory is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 193886688 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Hausdorff dimension of sets of numbers whose continued fractions contain arbitrarily long arithmetic progressions. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Nakajima%2C+Yuto%22">Nakajima, Yuto</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> yunakaji@mail.doshisha.ac.jp</i><br /><searchLink fieldCode="AR" term="%22Takahasi%2C+Hiroki%22">Takahasi, Hiroki</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> hiroki@math.keio.ac.jp</i><br /><searchLink fieldCode="AR" term="%22Wang%2C+Baowei%22">Wang, Baowei</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> bwei_wang@hust.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Number+Theory%22">Journal of Number Theory</searchLink>. Oct2026, Vol. 287, p72-94. 23p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Continued+fractions%22">Continued fractions</searchLink><br /><searchLink fieldCode="DE" term="%22Arithmetic+series%22">Arithmetic series</searchLink><br /><searchLink fieldCode="DE" term="%22Irrational+numbers%22">Irrational numbers</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+sequences%22">Mathematical sequences</searchLink><br /><searchLink fieldCode="DE" term="%22Fractal+dimensions%22">Fractal dimensions</searchLink><br /><searchLink fieldCode="DE" term="%22Fractals%22">Fractals</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Continued fractions with prescribed structures on sequences of their partial quotients have been intensively studied in the literature. As far as an integer sequence, especially a randomly generated one is concerned, an attractive question is whether it contains arbitrarily long arithmetic progressions. In this paper we study the fractal structure of irrational numbers whose sequences of partial quotients are strictly increasing and contain arbitrarily long, quantified arithmetic progressions. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Number Theory is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.jnt.2026.03.005 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 23 StartPage: 72 Subjects: – SubjectFull: Continued fractions Type: general – SubjectFull: Arithmetic series Type: general – SubjectFull: Irrational numbers Type: general – SubjectFull: Mathematical sequences Type: general – SubjectFull: Fractal dimensions Type: general – SubjectFull: Fractals Type: general Titles: – TitleFull: Hausdorff dimension of sets of numbers whose continued fractions contain arbitrarily long arithmetic progressions. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Nakajima, Yuto – PersonEntity: Name: NameFull: Takahasi, Hiroki – PersonEntity: Name: NameFull: Wang, Baowei IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: Oct2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 0022314X Numbering: – Type: volume Value: 287 Titles: – TitleFull: Journal of Number Theory Type: main |
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