Towards BAD conjecture
| dc.creator | Moshchevitin, Nikolay G. | |
| dc.date | 2007-12-14 | |
| dc.date | 2008-04-12 | |
| dc.date.accessioned | 2026-07-07T09:31:39Z | |
| dc.date.available | 2026-07-07T09:31:39Z | |
| dc.description | For $α, β, δ\in [0,1], α+β= 1 $ we consider sets $$ {\rm BAD}^* (α, β;δ) = \left\{ξ= (ξ_1,ξ_2) \in [0,1]^2: ,\inf_{p\in \mathbb{N}} \max \{(p\log(p+1))^α||pξ_1||, (p\log (p+1))^β||pξ_2||\} \ge δ\right\}. $$ We prove that for different $(α_1,β_1), (α_2,β_2), α_1 +β_1 = α_2 +β_2 = 1 $ and $δ$ small enough $$ {\rm BAD}^* (α_1, β_1 ;δ) \bigcap {\rm BAD}^* (α_2, β_2 ;δ) \neq \varnothing . $$ Our result is based on A. Khintchine's construction and an original method due to Y. Peres and W. Schlag. | |
| dc.description | Minor correction of errors in Lemma 2 | |
| dc.identifier | https://arxiv.org/abs/0712.2423 | |
| dc.identifier | http://arxiv.org/abs/0712.2423 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158537 | |
| dc.subject | Number Theory | |
| dc.title | Towards BAD conjecture | |
| dc.type | text |