A mass transference principle for systems of linear forms and its applications

作者：Allen Demi^*; Beresnevich Victor

来源：Compositio Mathematica, 2018, 154(5): 1014-1047.

DOI：10.1112/S0010437X18007121

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

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.

• 出版日期2018-5