| dc.creator | Otake, Shuichi | |
| dc.creator | Shaska, Tony | |
| dc.date | 2018-07-31 | |
| dc.identifier | http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2051 | |
| dc.identifier | 10.4067/S0719-06462018000200067 | |
| dc.description | Let 𝖿 ∈ ℝ(𝑡)[𝑥] be given by 𝖿(𝑡, 𝑥) = 𝑥𝑛 + 𝑡 · g(𝑥) and β1 < ··· < β𝑚 the distinct real roots of the discriminant ∆(𝖿,𝑥)(𝑡) of 𝖿(𝑡, 𝑥) with respect to 𝑥. Let γ be the number of real roots of
For any ξ > |βm|, if 𝑛−s is odd then the number of real roots of 𝖿(ξ,𝑥) is γ + 1, and if 𝑛−s is even then the number of real roots of 𝖿(ξ,𝑥) is γ, γ + 2 if ts > 0 or ts < 0 respectively. A special case of the above result is constructing a family of degree 𝑛 ≥ 3 irreducible polynomials over ℚ with many non-real roots and automorphism group S𝑛. | en-US |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.publisher | Universidad de La Frontera. Temuco, Chile. | en-US |
| dc.relation | http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2051/1831 | |
| dc.source | CUBO, A Mathematical Journal; Vol. 20 No. 2 (2018); 67–93 | en-US |
| dc.source | CUBO, A Mathematical Journal; Vol. 20 Núm. 2 (2018); 67–93 | es-ES |
| dc.source | 0719-0646 | |
| dc.source | 0716-7776 | |
| dc.subject | Polynomials | en-US |
| dc.subject | non-real roots | en-US |
| dc.subject | discriminant | en-US |
| dc.subject | Bezoutian | en-US |
| dc.subject | Galois groups | en-US |
| dc.title | Some remarks on the non-real roots of polynomials | en-US |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
