A Mahlers theorem for functions from words to integersReport as inadecuate




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

Abstract : In this paper, we prove an extension of Mahler-s theorem, 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* to Z, where d p is now the profinite metric defined by p-groups pro-p metric.


Keywords : Mahler p-adic automata profinite topology p-group





Author: Jean-Eric Pin - Pedro Silva -

Source: https://hal.archives-ouvertes.fr/



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