Related papers: On Jacobian conjecture

This paper has been withdrawn by the author(s), due a crucial error on the entanglement of $\Gamma$ registers.

This paper has been withdrawn by the author due to a crucial sign error in equation (5).

This paper has been withdrawn by the author, due to an error in the proof of Theorem 3.8.

We show that the Jacobian conjecture of the two dimensional case is true.

This paper is withdrawn from submission due to a critical error in the proof of main theorem.

This paper has been withdrawn by the author because Proposition 1 is not valid.

The paper has been withdrawn by the author, due to a critical error stemming from the defined template.

This paper has been withdrawn

The paper has been withdrawn by the author due to unhappy mistake in the initial scope of the work.

This paper has been retracted.

This paper has been withdrawn by the author due to a crucial error in the definition of homomorphism.

The paper has been withdrawn by the author due to a gap in Proof of Theorem 1.1.

The paper is withdrawn due to an error in Section 2.

This paper has been withdrawn by the author(s), due a crucial i-number error in Eqn. 18.

The paper has been withdrawn.

This paper has been withdrawn while the author verifies the literature.

This paper has been withdrawn by the author, due a crucial mistake in proof of lemma 4.2.

Withdrawn. We thank J. T. Liu for bringing an error in the manuscript to our attention.

This paper has been withdrawn by the author because Lemma 3 is incorrect. This mistake is crucial in this paper.

This paper has been withdrawn due to crucial erros in equations (24)--(31).