Schmidt's theorem, Hausdorff measures and Slicing
| dc.creator | Beresnevich, Victor | |
| dc.creator | Velani, Sanju | |
| dc.date | 2005-07-18 | |
| dc.date.accessioned | 2026-07-07T05:21:49Z | |
| dc.date.available | 2026-07-07T05:21:49Z | |
| dc.description | A Hausdorff measure version of W.M. Schmidt's inhomogeneous, linear forms theorem in metric number theory is established. The key ingredient is a `slicing' technique motivated by a standard result in geometric measure theory. In short, `slicing' together with the Mass Transference Principle [3] allows us to transfer Lebesgue measure theoretic statements for limsup sets associated with linear forms to Hausdorff measure theoretic statements. This extends the approach developed in [3] for simultaneous approximation. Furthermore, we establish a new Mass Transference Principle which incorporates both forms of approximation. As an application we obtain a complete metric theory for a `fully' non-linear Diophantine problem within the linear forms setup. [3] V. Beresnevich and S. Velani : A Mass Transference Principle and the Duffin--Schaeffer conjecture for Hausdorff measures, Pre-print (22pp): arkiv:math.NT/0401118. To appear: Annals of Math. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/math/0507369 | |
| dc.identifier | http://arxiv.org/abs/math/0507369 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75826 | |
| dc.subject | Number Theory | |
| dc.subject | 11J83;28A78 | |
| dc.title | Schmidt's theorem, Hausdorff measures and Slicing | |
| dc.type | text |