Approximation to real numbers by cubic algebraic integers II
| dc.creator | Roy, Damien | |
| dc.date | 2002-10-11 | |
| dc.date | 2002-10-24 | |
| dc.date.accessioned | 2026-07-07T04:51:52Z | |
| dc.date.available | 2026-07-07T04:51:52Z | |
| dc.description | It has been conjectured for some time that, for any integer n\ge 2, any real number ε>0 and any transcendental real number ξ, there would exist infinitely many algebraic integers αof degree at most n with the property that |ξ-α| < H(α)^{-n+ε}, where H(α) denotes the height of α. Although this is true for n=2, we show here that, for n=3, the optimal exponent of approximation is not 3 but (3+\sqrt{5})/2 = 2.618... | |
| dc.description | 7 pages; major simplification of the original proof | |
| dc.identifier | https://arxiv.org/abs/math/0210182 | |
| dc.identifier | http://arxiv.org/abs/math/0210182 | |
| dc.identifier | Annals of Mathematics 158 (2003), 1081-1087. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65263 | |
| dc.subject | Number Theory | |
| dc.subject | 11J04;11J82 | |
| dc.title | Approximation to real numbers by cubic algebraic integers II | |
| dc.type | text |