Related papers: Ambiguous ideal classes and ambiguous ideals

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This paper was withdrawn by the author. It turns out that similar ideas have been presented before. The author apologizes.

This paper has been withdrawn by the author, due to an error in Proposition 2.2.

We withdraw the paper because the results are wrong.

This paper has been withdrawn by the author due to a crucial argument error at p.10.

This paper has been withdrawn by the author due to a gap in the proof of Lemma 3.4

This article has been withdrawn by arXiv administrators due to plagiarized content from arXiv:1010.2469.

This paper has been withdrawn by the author due to an error in the derivation.

The paper was withdrawn by the author. It contained various errors.

This paper has been withdrawn by the author due to an error in an inequality in the proof of Theorem 1.1.

There have been gaps found in the proofs. The paper is withdrawn until further notice.

This paper has been withdrawn by the author due to a mistake in the proof of the main theorem.

This paper has been withdrawn at the author's request.

This paper has been withdrawn by the author: it was a too preliminary version.

This paper has been withdrawn by the author(s), due a crucial sign error in conclusion .

This paper has been withdrawn by the author because eq.(4) and those subsequent are incorrect.

This paper has been withdrawn.

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This paper has been withdrawn temporarily.

This paper has been withdrawn because the content has been substantially improved in a later paper, arXiv:0806.1165.