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Does anyone know of a p-adic analogue of Liouville's approximation theorem http://mathworld.wolfram.com/LiouvillesApproximationTheorem.html with proof?

I'm aware of Roth's theorem and subspace theorems which can be generalized to p-adic numbers, these are different in that the constants are not effective.

edited May 5 2012 at 8:31

asked May 5 2012 at 5:57

Kale
99●2

	Anatoly: Is this the only paper on the subject? It looks like it's generalized over any extension field. – Kale May 5 2012 at 8:33
	I'm intereste in ways that ordinary Liouville's theorem relates to p-adic Liouville's theorem – Kale May 5 2012 at 8:51
	So far I found only this one. – Anatoly Kochubei May 5 2012 at 9:10

Anatoly Kochubei · Answer 1 · 2012-05-05 06:19:09Z UTC

2

See the paper by J.-H. Evertse, http://www.math.leidenuniv.nl/~evertse/99-sym.pdf

answered May 5 2012 at 6:19

Anatoly Kochubei
3,052●1●4●9

p-adic version of Liouville’s approximation theorem

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