Related papers: A note on the Jacobian Conjecture

Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.

The said paper [2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is with gaps.

withdrawed due to a substantial error.

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

Using the author's inversion formula for automorphisms of the Weyl algebras with polynomial coefficients and the bound on its degree a slightly shorter (algebraic) proof is given of the result of A. Belov-Kanel and M. Kontsevich that the…

This paper has been withdrawn by the authors due to an error in Section 7.

We first propose what we call the Gaussian Moments Conjecture. We then show that the Jacobian Conjecture follows from the Gaussian Moments Conjecture. We also give a counter-example to a more general statement known as the Moments Vanishing…

This paper has been withdrawn by the author, due an error in the proof of Proposion 2.13.

The Jacobian conjecture is an old unsolved problem in mathematics, which has been unsuccessfully attacked from many different angles. We add here another point of view pertaining to the so called formal inverse approach, that of…

One of the aims of this article is to provide a class of polynomial mappings for which the Jacobian conjecture is true. Also, we state and prove several global univalence theorems and present a couple of applications of them.

An elementary gap in the proof of corollary 2.2 was found, the claim in the first version of the paper is thus retracted.

Let $F:\mathbb{C}[x_1,\ldots,x_n] \to \mathbb{C}[x_1,\ldots,x_n]$ be a $\mathbb{C}$-algebra endomorphism that has an invertible Jacobian. We bring two ideas concerning the Jacobian Conjecture: First, we conjecture that for all $n$, the…

We prove that the Dimension Conjecture implies the Jacobi Bound Conjecture.

This paper has been withdrawn by the author due to an erro thereon line -2 of page 4.

Jacobian conjecture states that if $F:\ \mathbb C^n(\mathbb R^n)\rightarrow \mathbb C^n(\mathbb R^n)$ is a polynomial map such that the Jacobian of $F$ is a nonzero constant, then $F$ is injective. This conjecture is still open for all…

The said paper [Su2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is false.

We prove that the Jacobian conjecture is false if and only if there exists a solution to a certain system of polynomial equations. We analyse the solution set of this system. In particular we prove that it is zero dimensional.

It is shown that the $n$-dimensional Jacobian conjecture over algebraic number fields may be considered as an existence problem of integral points on affine curves. More specially, if the Jacobian conjecture over $\mathbb{C}$ is false, then…

The Jacobian conjecture involves the map $y= x - V(x)$ where $y, x$ are n-dimensional vectors, $V(x)$ is a symmetric polynomial of degree $d$ for which the Jacobian hypothesis holds: $ e^{Tr \ln(1- V'(x))} =1,\ \forall x$. The conjecture…

The Jacobian conjecture is a well-known open problem in affine algebraic geometry that asks if any polynomial endomorphism of the affine space $\mathbb{A}_{\mathbb{C}}^{n}$ ($n\geq2$) with jacobian $1$ is an automorphism. We present a…