An overview of some recent developments on integer-valued polynomials: Answers and Questions

Chabert, Jean-Luc

Actes des rencontres du CIRM, Tome 2 (2010) no. 2, pp. 3-14.

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.

Classification : 13F20
Mots clés : Integer-valued polynomials, Pólya fields, Prüfer domains, $p$-orderings, Quaternions, Bernoulli numbers, ultrametric analysis, discrete dynamical systems

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