Chow, Samuel Khai Ho (2018) Bohr sets and multiplicative diophantine approximation. Duke Mathematical Journal. pp. 1623-1642. ISSN 0012-7094
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 fibre 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 generalised arithmetic progressions within inhomogeneous Bohr sets, extending a construction given by Tao. This precise structure enables us to verify the hypotheses of the Duffin--Schaeffer theorem for the problem at hand, via the geometry of numbers.
Metadata
Authors/Creators: |
|
---|---|
Copyright, Publisher and Additional Information: | This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details. |
Keywords: | metric diophantine approximation, additive combinatorics, geometry of numbers |
Dates: |
|
Institution: | The University of York |
Academic Units: | The University of York > Faculty of Sciences (York) > Mathematics (York) |
Depositing User: | Pure (York) |
Date Deposited: | 15 Jan 2018 13:20 |
Last Modified: | 06 Dec 2023 12:14 |
Published Version: | https://doi.org/10.1215/00127094-2018-0001 |
Status: | Published |
Refereed: | Yes |
Identification Number: | https://doi.org/10.1215/00127094-2018-0001 |
Related URLs: |
Download
Filename: BohrSetsAndMultiplicativeDiophantineApproximation_171203.pdf
Description: BohrSetsAndMultiplicativeDiophantineApproximation_171203