A Mass Transference Principle for systems of linear forms and its applications

Demi Denise Allen, Victor Beresnevich

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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.

Original languageEnglish
Pages (from-to)1014-1047
Number of pages34
JournalCompositio Mathematica
Issue number5
Early online date3 Apr 2018
Publication statusPublished - 1 May 2018

Bibliographical note

© The Authors 2018.


  • Diophantine approximation
  • Hausdorff measures
  • Khintchine-Groshev theorem
  • mass transference principle

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