Related papers: A quantitative version of the Roth-Ridout theorem

This paper has been withdrawn by the author due to a crucial error in Lemma 3.5.

The paper has been withdrawn by the author due to a gap in Proof of Theorem 1.1.

This paper has been withdrawn by the author due to a crucial error in last part of proof.

This paper has been withdrawn by the authors due to an error.

This paper has been withdrawn by the author due to a crucial error in the proof of Lemma 2.2.

This paper has been withdrawn by the author, due to an error in the proof of Theorem 3.8.

This paper has been withdrawn by the author because there are some typos in proofs.

This paper has been withdrawn by the authors because M. Aschenbrenner pointed out that the proof of theorem 3.1 was incorrect.

This paper has been withdrawn due to a crucial theoretical error.

This paper has been withdrawn by the author due to a crucial problem in Lemma 3. This equation must be changed.

This paper has been withdrawn by the authors due to a crucial error.

This paper has been withdrawn by the author due to a crucial sign error in Theorem 3.4.

This paper has been withdrawn by the author due to a crucial sign error in equation 1.

This paper has been withdrawn by the author due to a serious mistake on Lemma 2.4.

This paper has been withdrawn while the author verifies the literature.

This paper has been withdrawn by the author due to an error in an inequality in the proof of Theorem 1.1.

The paper has been withdrawn by the author, due to it being fundamentally flawed. The author apologizes for any inconvenience it may have caused.

This paper is withdrawn. We found a mistake in Lemma 4.1

The paper has been withdrawn due to numerical error.

This paper has been withdrawn by the author due to the incorrect argument for the security.