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A mass transference principle for systems of linear forms and its applications
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Allen, Demi and Beresnevich, Victor (2018) A mass transference principle for systems of linear forms and its applications. Compositio Mathematica, 154 (5). pp. 1014-1047. doi:10.1112/S0010437X18007121 ISSN 0010-437X.
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Official URL: http://dx.doi.org/10.1112/S0010437X18007121
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.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Journal or Publication Title: | Compositio Mathematica | ||||||
| Publisher: | Cambridge University Press | ||||||
| ISSN: | 0010-437X | ||||||
| Official Date: | May 2018 | ||||||
| Dates: |
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| Volume: | 154 | ||||||
| Number: | 5 | ||||||
| Page Range: | pp. 1014-1047 | ||||||
| DOI: | 10.1112/S0010437X18007121 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Open Access (Creative Commons) |
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