A Gel'fond type criterion in degree two

dc.creatorArbour, Benoit
dc.creatorRoy, Damien
dc.date2002-12-16
dc.date.accessioned2026-07-07T04:53:49Z
dc.date.available2026-07-07T04:53:49Z
dc.descriptionWe establish a criterion for a complex number to be algebraic over Q of degree at most two. It requires that, for any sufficiently large real number X, there exists a non-zero polynomial with integral coefficients, of degree at most two and height at most X, whose absolute value at that complex number is at most (1/4)X^{-(3+sqrt{5})/2}. We show that the exponent (3+sqrt{5})/2 in this condition is optimal, and deduce from this criterion a result of simultaneous approximation of a real number by conjugate algebraic numbers.
dc.description6 pages
dc.identifierhttps://arxiv.org/abs/math/0212209
dc.identifierhttp://arxiv.org/abs/math/0212209
dc.identifierActa Arithmetica 111.1 (2004), 97-103
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/66001
dc.subjectNumber Theory
dc.subject11J13
dc.titleA Gel'fond type criterion in degree two
dc.typetext

Files

Collections