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Bohr sets and multiplicative Diophantine approximation

Abstract:

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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Publisher copy:
10.1215/00127094-2018-0001

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Department:
Unknown
Role:
Author
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Funding agency for:
Chow, S
Grant:
DMS-1440140
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:
1547-7398
ISSN:
0012-7094
Keywords:
Pubs id:
pubs:926122
UUID:
uuid:c6172c02-fb01-4f8c-8936-139cb6d30721
Local pid:
pubs:926122
Source identifiers:
926122
Deposit date:
2018-10-10

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