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Spécialisation de la suite de Sturm

Laureano González-Vega, Henri Lombardi, Tomas Recio, Marie-Françoise Roy (1994)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Specializations of one-parameter families of polynomials

Farshid Hajir, Siman Wong (2006)

Annales de l’institut Fourier

Let K be a number field, and suppose λ ( x , t ) K [ x , t ] is irreducible over K ( t ) . Using algebraic geometry and group theory, we describe conditions under which the K -exceptional set of λ , i.e. the set of α K for which the specialized polynomial λ ( x , α ) is K -reducible, is finite. We give three applications of the methods we develop. First, we show that for any fixed n 10 , all but finitely many K -specializations of the degree n generalized Laguerre polynomial L n ( t ) ( x ) are K -irreducible and have Galois group S n . Second, we study specializations...

Spherical completeness with infinitesimals.

José Manuel Bayod (1982)

Revista Matemática Hispanoamericana

In the theory of nonarchimedean normed spaces over valued fields other than R or C, the property of spherical completeness is of utmost importance in several contexts, and it appears to play the role conventional completeness does in some topics of classical functional analysis. In this note we give various characterizations of spherical completeness for general ultrametric spaces, related to but different from the notions of pseudo-convergent sequence and pseudo-limit introduced by Ostrowski in...

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