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A Mahler's theorem for functions from words to integers

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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).

BibTeX - Entry

@InProceedings{pin_et_al:LIPIcs:2008:1321,
  author =	{Jean-Eric Pin and Pedro V. Silva},
  title =	{{A Mahler's theorem for functions from words to integers}},
  booktitle =	{25th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{585--596},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-06-4},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{1},
  editor =	{Susanne Albers and Pascal Weil},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2008/1321},
  URN =		{urn:nbn:de:0030-drops-13212},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.STACS.2008.1321},
  annote =	{Keywords: $p$-adic topology, binomial coefficients, Mahler's theorem, $p$-group languages}
}

Keywords: $p$-adic topology, binomial coefficients, Mahler's theorem, $p$-group languages
Seminar: 25th International Symposium on Theoretical Aspects of Computer Science
Issue date: 2008
Date of publication: 2008


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