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

Jean-Luc Chabert

doi:10.5802/acirm.27

Jean-Luc Chabert ¹

¹ Départment de Mathématiques Université de Picardie 80039 Amiens, France LAMFA CNRS-UMR 6140

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

Abstract

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.

Published online: 2011-10-19

Zbl: 06938575

DOI: 10.5802/acirm.27

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

Author's affiliations:

Jean-Luc Chabert ¹

¹ Départment de Mathématiques Université de Picardie 80039 Amiens, France LAMFA CNRS-UMR 6140

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Jean-Luc Chabert. An overview of some recent developments on integer-valued polynomials: Answers and Questions. Actes des rencontres du CIRM, Volume 2 (2010) no. 2, pp. 3-14. doi : 10.5802/acirm.27. https://acirm.centre-mersenne.org/articles/10.5802/acirm.27/

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