A noncommutative extension of Mahler's theorem on interpolation series

Jean-Eric Pin (1) , Pedro Silva (2)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 CMUP - Centro de Matemática, Faculdade de Ciências

In this paper, we prove an extension of Mahler's theorem on interpolation series, a celebrated result of p-adic analysis. Mahler's original result states that a function from N to Z is uniformly continuous for the p-adic metric d_p if and only if it can be uniformly approximated by polynomial functions. We prove the same result for functions from a free monoid A* to Z, where d_p is replaced by the pro-p metric, the profinite metric on A* defined by p-groups.

Mots clés: p-adic topology; binomial coefficients; Mahler's theorem; p-group languages

Domaines: Autre [cs.OH]; Théorie des nombres [math.NT]; Combinatoire [math.CO]

Jean-Eric Pin, Pedro Silva. A noncommutative extension of Mahler's theorem on interpolation series. 2011. ⟨hal-00654030⟩