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.