Approximation to real numbers by cubic algebraic integers II

dc.creatorRoy, Damien
dc.date2002-10-11
dc.date2002-10-24
dc.date.accessioned2026-07-07T04:51:52Z
dc.date.available2026-07-07T04:51:52Z
dc.descriptionIt 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.description7 pages; major simplification of the original proof
dc.identifierhttps://arxiv.org/abs/math/0210182
dc.identifierhttp://arxiv.org/abs/math/0210182
dc.identifierAnnals of Mathematics 158 (2003), 1081-1087.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65263
dc.subjectNumber Theory
dc.subject11J04;11J82
dc.titleApproximation to real numbers by cubic algebraic integers II
dc.typetext

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