A mass transference principle for systems of linear forms and its applications.(English)Zbl 1404.11097
The authors prove a general mass transfer principle for systems of linear forms. This settles a conjecture of the second author andS. Velani [Int. Math. Res. Not. 2006, No. 19, Article ID 48794, 24 p. (2006;Zbl 1111.11037)] where such a principle was established under additional technical conditions. Furthermore, the authors present various applications to problems in Diophantine approximation, in particular to Khintchine-Groshev type theorems for Hausdorff measure. The method works in the homogeneous as well as in the inhomogeneous case. Also approximation by primitive points and other coprimality conditions in the spirit ofS. G. Dani et al. [Math. Z. 279, No. 3–4, 1081–1101 (2015;Zbl 1311.11062)] are considered. The paper concludes with a detailed presentation of the proof of the main theorem, including the necessary auxiliary results, such as an important covering lemma.
Reviewer: Robert F. Tichy (Graz)
MSC:
| 11J83 | Metric theory |
| 28A78 | Hausdorff and packing measures |
| 11J13 | Simultaneous homogeneous approximation, linear forms |
Keywords:
Diophantine approximation;mass transference principle;Khintchine-Groshev theorem;Hausdorff measuresCite
References:
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