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DOI: 10.4230/LIPIcs.STACS.2008.1321
URN: urn:nbn:de:0030-drops-13212
URL: https://drops.dagstuhl.de/opus/volltexte/2008/1321/
Pin, Jean-Eric ; Silva, Pedro V.
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, acelebrated 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 = {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: | 06.02.2008 |
