Allen, Demi Denise and Beresnevich, Victor orcid.org/0000-0002-1811-9697 (2018) A Mass Transference Principle for systems of linear forms and its applications. Compositio Mathematica. pp. 1014-1047. ISSN 1570-5846
Abstract
In this paper we establish a general form of the mass transference principle for systems of linear forms conjectured in 2009. We also present a number of applications of this result to problems in Diophantine approximation. These include a general transference of Lebesgue measure Khintchine-Groshev type theorems to Hausdorff measure statements. The statements we obtain are applicable in both the homogeneous and inhomogeneous settings as well as allowing transference under any additional constraints on approximating integer points. In particular, we establish Hausdorff measure counterparts of some Khintchine-Groshev type theorems with primitivity constraints recently proved by Dani, Laurent and Nogueira.
Metadata
Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Authors 2018. |
Keywords: | Diophantine approximation, Hausdorff measures, Khintchine-Groshev theorem, mass transference principle |
Dates: |
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Institution: | The University of York |
Academic Units: | The University of York > Faculty of Sciences (York) > Mathematics (York) |
Depositing User: | Pure (York) |
Date Deposited: | 20 Dec 2017 14:30 |
Last Modified: | 06 Dec 2023 12:12 |
Published Version: | https://doi.org/10.1112/S0010437X18007121 |
Status: | Published |
Refereed: | Yes |
Identification Number: | https://doi.org/10.1112/S0010437X18007121 |
Related URLs: |
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Description: A mass transference principle for systems of linear
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