A Gel'fond type criterion in degree two
| dc.creator | Arbour, Benoit | |
| dc.creator | Roy, Damien | |
| dc.date | 2002-12-16 | |
| dc.date.accessioned | 2026-07-07T04:53:49Z | |
| dc.date.available | 2026-07-07T04:53:49Z | |
| dc.description | We 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.description | 6 pages | |
| dc.identifier | https://arxiv.org/abs/math/0212209 | |
| dc.identifier | http://arxiv.org/abs/math/0212209 | |
| dc.identifier | Acta Arithmetica 111.1 (2004), 97-103 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66001 | |
| dc.subject | Number Theory | |
| dc.subject | 11J13 | |
| dc.title | A Gel'fond type criterion in degree two | |
| dc.type | text |