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Counting multiplicative approximations
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Chow, Sam and Technau, Niclas (2023) Counting multiplicative approximations. The Ramanujan Journal, 62 . pp. 241-250. doi:10.1007/s11139-022-00610-3 ISSN 1382-4090.
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Official URL: https://doi.org/10.1007/s11139-022-00610-3
Abstract
A famous conjecture of Littlewood (c. 1930) concerns approximating two real numbers by rationals of the same denominator, multiplying the errors. In a lesser-known paper, Wang and Yu (1981) established an asymptotic formula for the number of such approximations, valid al-most always. Using the quantitative Koukoulopoulos–Maynard theorem of Aistleitner–Borda–Hauke, together with bounds arising from the theory of Bohr sets, we deduce lower bounds of the expected order of magnitude for inhomogeneous and fibre refinements of the problem.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Diophantine approximation, Multiplicity (Mathematics) | ||||||||
Journal or Publication Title: | The Ramanujan Journal | ||||||||
Publisher: | Springer | ||||||||
ISSN: | 1382-4090 | ||||||||
Official Date: | September 2023 | ||||||||
Dates: |
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Volume: | 62 | ||||||||
Page Range: | pp. 241-250 | ||||||||
DOI: | 10.1007/s11139-022-00610-3 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Reuse Statement (publisher, data, author rights): | This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s11139-022-00610-3 | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 20 June 2022 | ||||||||
Date of first compliant Open Access: | 18 August 2023 | ||||||||
RIOXX Funder/Project Grant: |
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