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



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.


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 



The author thanks the anonymous referee for many valuable suggestions.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.LAMFA CNRS-UMR 7352Université de PicardieAmiensFrance

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