Chapter

Commutative Algebra

pp 83-111

Date:

Integer-Valued Polynomials: Looking for Regular Bases (A Survey)

  • Jean-Luc ChabertAffiliated withLAMFA CNRS-UMR 7352, Université de Picardie Email author 

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Abstract

This paper reviews recent results about the additive structure of algebras of integer-valued polynomials and, particularly, the question of the existence and the construction of regular bases. Doing this, we will be led to consider questions of combinatorial, arithmetical, algebraic, ultrametric, or dynamical nature.

Keywords

Integer-valued polynomials Generalized factorials v-Orderings Kempner’s formula Regular basis Pólya fields Divided differences Mahler’s theorem

2010 MSC

Primary 13F20 Secondary 11S05 11R21 11B65