De quelques propositions sur les nombres
Sur une publication de P. Ribenboim.
Anneaux de Fatou
Le Nullstellensatz de Hilbert et les Polynomes à Valeurs Entières.
Ideaux de polynomes et ideaux de valeurs.
Polynomes à valeurs entières et propriété de Skolem.
Les idéaux premiers de l'anneau des polynomes à valeurs entières.
Dérivées et différences divisées à valeurs entières
Anneaux de 'polynômes à valeurs entières' et anneaux de Fatou
Polynômes à valeurs entières ainsi que leurs dérivées
An overview of some recent developments on integer-valued polynomials: Answers and Questions
The purpose of my talk is to give an overview of some more or less recent developments on integer-valued polynomials and, doing so, to emphasize that integer-valued polynomials really occur in different areas: combinatorics, arithmetic, number theory, commutative and non-commutative algebra, topology, ultrametric analysis, and dynamics. I will show that several answers were given to open problems, and I will raise also some new questions.
Permanence properties of the Baum-Connes conjecture.
The Connes-Kasparov conjecture for almost connected groups and for linear -adic groups
Let G be a locally compact group with cocompact connected component. We prove that the assembly map from the topological K-theory of G to the K-theory of the reduced C-algebra of G is an isomorphism. The same is shown for the groups of -rational points of any linear algebraic group over a local field of characteristic zero.
On the ultrametric Stone-Weierstrass theorem and Mahler's expansion
We describe an ultrametric version of the Stone-Weierstrass theorem, without any assumption on the residue field. If is a subset of a rank-one valuation domain , we show that the ring of polynomial functions is dense in the ring of continuous functions from to if and only if the topological closure of in the completion of is compact. We then show how to expand continuous functions in sums of polynomials.
An extension of the Lucas theorem
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