MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question
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 '12 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 '12 at 6:26
If you have access to a library, you could look into interlibrary loan. – Gerry Myerson May 4 '12 at 12:18

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

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

Often these papers cannot be found by standard search englines.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.