2026-07-24T11:54:13Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:1321 2024-03-06T10:33:02Z ddc:004 open_access

A Mahler's theorem for functions from words to integers Pin, Jean-Eric Silva, Pedro V. $p$-adic topology binomial coefficients Mahler's theorem $p$-group languages 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). Schloss Dagstuhl – Leibniz-Zentrum für Informatik Jean-Eric Pin and Pedro V. Silva 2008 Is Part Of LIPIcs, Volume 1, 25th International Symposium on Theoretical Aspects of Computer Science (2008) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2008.1321 urn:nbn:de:0030-drops-13212 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1321 eng https://creativecommons.org/licenses/by-nd/3.0/legalcode