ON THE IRREDUCIBILITY OF THE POLYNOMIALS P(T(M),Y)

被引：17

作者：

DEBES, P

机构：

[1] Institut Henri Poincaré, 75231 Paris Cedex 05, 11, rue Pierre et Marie Curie

来源：

JOURNAL OF NUMBER THEORY | 1992年 / 42卷 / 02期

关键词：

D O I：

10.1016/0022-314X(92)90018-K

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We characterize the polynomials P(X, Y) that are irreducible over a number field K and such that for some t ∈ K, the specialized polynomials P(tm, Y) are reducible in K[Y] for infinitely many integers m. As a consequence, we show for example that if P is absolutely irreducible and if t is neither a strict power in K nor of the form -4w4 or -w2 with w ∈ K, then P(tm, Y) is irreducible in K[Y] for infinitely many integers m (cf. Corollary 1.8). © 1992.

引用

页码：141 / 157

页数：17