Journal article
Bohr sets and multiplicative Diophantine approximation
- Abstract:
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In two dimensions, Gallagher’s theorem is a strengthening of the Littlewood conjecture that holds for almost all pairs of real numbers. We prove an inhomogeneous fiber version of Gallagher’s theorem, sharpening and making unconditional a result recently obtained conditionally by Beresnevich, Haynes, and Velani. The idea is to find large generalized arithmetic progressions within inhomogeneous Bohr sets, extending a construction given by Tao. This precise structure enables us to verify the hyp...
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- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
-
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(Accepted manuscript, pdf, 348.8KB)
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- Publisher copy:
- 10.1215/00127094-2018-0001
Authors
Funding
+ Engineering and Physical Sciences
Research Council
More from this funder
Funding agency for:
Chow, S
Grant:
DMS-1440140
Bibliographic Details
- Publisher:
- Duke University Press Publisher's website
- Journal:
- Duke Mathematical Journal Journal website
- Volume:
- 167
- Issue:
- 9
- Pages:
- 1623-1642
- Publication date:
- 2018-03-23
- DOI:
- EISSN:
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1547-7398
- ISSN:
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0012-7094
Item Description
- Keywords:
- Pubs id:
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pubs:926122
- UUID:
-
uuid:c6172c02-fb01-4f8c-8936-139cb6d30721
- Local pid:
- pubs:926122
- Source identifiers:
-
926122
- Deposit date:
- 2018-10-10
Terms of use
- Copyright holder:
- Duke University Press
- Copyright date:
- 2018
- Notes:
- This is the accepted manuscript version of the article. The final version is available online from Duke University Press at: https://doi.org/10.1215/00127094-2018-0001
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