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

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Publication details

JournalCompositio Mathematica
DateAccepted/In press - 19 Dec 2017
DateE-pub ahead of print - 3 Apr 2018
DatePublished (current) - 1 May 2018
Issue number5
Number of pages34
Pages (from-to)1014-1047
Early online date3/04/18
Original languageEnglish


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.

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© The Authors 2018.

    Research areas

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

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