Sur le spectre d'un polynôme à plusieurs variables
Sur l'équation du troisième degré
Sur les modules des zéros des polynômes
Sur les zéros réels des polynômes de Bernoulli
Nous donnons les démonstrations détaillées des résultats énoncés dans une note de même titre (C. R. Acad. Sci., Paris, Ser. I 303 (1986), 539–542).Ces résultats concernent le nombre et la position des zéros réels des polynômes de Bernoulli.
Sur un théorème de M. Laguerre
Sur une distribution de zéros
Sur une propriété des déterminants fonctionnels et son application au développement des fonctions implicites.
Szegö,G., Bemerkungen zu einer Arbeit von Herrn M. Fekete: Über die Ver-teilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahligen Koeffizienten
The absolute Galois group of a pseudo real closed field
The Boolean space of higher level orderings
Let K be an ordered field. The set X(K) of its orderings can be topologized to make it a Boolean space. Moreover, it has been shown by Craven that for any Boolean space Y there exists a field K such that X(K) is homeomorphic to Y. Becker's higher level ordering is a generalization of the usual concept of ordering. In a similar way to the case of ordinary orderings one can define a topology on the space of orderings of fixed exact level. We show that it need not be Boolean. However, our main theorem...
The factorization of certain quadrinominals.
The Fekete-Szegő theorem with splitting conditions: Part II
The field of Nash functions and factorization of polynomials
The algebraically closed field of Nash functions is introduced. It is shown that this field is an algebraic closure of the field of rational functions in several variables. We give conditions for the irreducibility of polynomials with Nash coefficients, a description of factors of a polynomial over the field of Nash functions and a theorem on continuity of factors.
The formal inverse and the Jacobian Conjecture
The Galois Cohomology of Pythagorean Fields.
The Hilbert Modular Surface of a Real Quadratic Field.
The identity of three classes of polynomials.
The intersection theorem for orderings of higher level in rings.
The Lehmer constants of an annulus
Let be the Mahler measure of an algebraic number , and be an open subset of . Then its Lehmer constant is inf , the infimum being over all non-zero non-cyclotomic lying with its conjugates outside . We evaluate when is any annulus centered at . We do the same for a variant of , which we call the transfinite Lehmer constant .Also, we prove the converse to Langevin’s Theorem, which states that if contains a point of modulus . We prove the corresponding result for .
The Lojasiewicz exponent at infinity for overdetermined polynomial mappings
We prove that the study of the Łojasiewicz exponent at infinity of overdetermined polynomial mappings , m > n, can be reduced to the one when m = n.