Related papers: Endomorphisms of polynomial rings and Jacobians

This paper has been withdrawn by the author due to a error in attachment of source file.

This paper has been withdrawn by the author due to a crucial sign error in Proposition 3.1.

This paper has been withdrawn by the author due to a crucial error in last part of proof.

This paper has been withdrawn by the author due to a mistake in the section 4.

This paper has been withdrawn by the author due to a crucial sign error in equation 1.

This paper has been withdrawn by the author due to a crucial sign error in equation 1.

This paper has been withdrawn by the author due to an error in the derivation.

This paper has been withdrawn by the author. It will be replaced, substantially modified, by sections of the author's completed PhD thesis.

This paper has been withdrawn by the author, due a crucial error in Eq. 6.

The author decided to withdraw this paper by 1) an error in Lemma 5.11 (and 5.12) which requires some justification; 2) the main result of this paper suffers overlap with arXiv:1203.5254; 3) the author decided to split arXiv:1203.5254 into…

The paper has been withdrawn.

This paper was withdrawn by the author due to an edition's rights

The paper has been withdrawn due to an error in the main theorem.

This paper has been withdrawn by the author due to a crucial sign error in equation 1

This paper has been withdrawn by the author, due to errors in Groebner basis calculations in the cases of five and six dimensional groups.

This paper has been withdrawn due to an error in the proof of Theorem 5.3.

This paper has been withdrawn by the authors due to some errors.

This paper has been withdrawn by the authors due to the crucial wrong assumption following Eq. 9.

This paper has been withdrawn by the author, due a crucial error in the optimization. For the last one month I have been trying to remove the error, but it seems to take a lot of time so I decided to withdraw this paper for the moment.

This paper has been withdrawn by the author due to the incorrect argument for the security.