A Mass Transference Principle for systems of linear forms and its applications
نویسندگان
چکیده
In this paper we establish a general form of the Mass Transference Principle for systems of linear forms conjectured in [1]. We also present a number of applications to problems in Diophantine approximation. These include a general transference of Khintchine–Groshev type theorems into Hausdorff measure statements. These statements are applicable in both the homogeneous and inhomogeneous settings and allow transference under any additional constraints on approximating integer points. In particular, we establish Hausdorff measure counterparts of the Khintchine– Groshev type theorems with primitivity constraints recently proved by Dani, Laurent and Nogueira [8]. 2000 Mathematics Subject Classification: Primary 11J83, 28A78; Secondary 11J13, 11K60
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