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Suppose you have a sequence of rational numbers that gives a diophantine approximaion an irrational, what can be said p-adically about this sequence?

I'm interested in the p-adic analoges of these theorems (such as Thue-siegel-roth), but can't find any straightforward resources on the subject. I can't even find what a good diophantine approximation would mean over a p-adic field.

flag	asked May 4 2012 at 5:31 Kale 99●2

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The $p$-adic theory is quite well developed. See, for example, the paper of D. Ridout "The p-adic generalization of the Thue-Siegel-Roth theorem", Mathematika 5 1958 40–48. Schlickewei has proved a $p$-adic version of Schmidt's theorem, see "Linearformen mit algebraischen koeffizienten", Manuscripta Math. 18 (1976), no. 2, 147–185. – ulrich May 4 2012 at 6:11

I'm aware of these particular references listed on the wikipedia page, the problem is I can't find them anywhere. – Kale May 4 2012 at 6:26

If you have access to a library, you could look into interlibrary loan. – Gerry Myerson May 4 2012 at 12:18

Anatoly Kochubei · Answer 1 · 2012-05-04 13:38:04Z UTC

The paper by Schlickewei mentioned in the comment is available here:

http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN365956996_0018&DMDID=DMDLOG_0012

In general, many old mathematical papers can be obtained free of charge via the site

http://www.emani.org/

Often these papers cannot be found by standard search englines.

p-adic diophantine approximation

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