Specializations of one-parameter families of polynomials
| dc.creator | Hajir, Farshid | |
| dc.creator | Wong, Siman | |
| dc.date | 2004-05-07 | |
| dc.date.accessioned | 2026-07-07T05:08:02Z | |
| dc.date.available | 2026-07-07T05:08:02Z | |
| dc.description | Let K be a number field, and let lambda(x,t)\in K[x, t] be irreducible over K(t). Using algebraic geometry and group theory, we study the set of alpha\in K for which the specialized polynomial lambda(x,alpha) is K-reducible. We apply this to show that for any fixed n>=10 and for any number field K, all but finitely many K-specializations of the degree n generalized Laguerre polynomial are K-irreducible and have Galois group S_n. In conjunction with the theory of complex multiplication, we also show that for any K and for any n>=53, all but finitely many of the K-specializations of the modular equation Phi_n(x, t) are K-irreducible and have Galois group containing PSL_2(Z/n). | |
| dc.identifier | https://arxiv.org/abs/math/0405139 | |
| dc.identifier | http://arxiv.org/abs/math/0405139 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71099 | |
| dc.subject | Number Theory | |
| dc.subject | 12H25 | |
| dc.title | Specializations of one-parameter families of polynomials | |
| dc.type | text |