10 citations · 32 across the 11 of their papers we have counts for
13 papers
An elementary way to find a counterexample to the Jacobian Conjecture
Arno van den Essen
We show how a counterexample to the Jacobian Conjecture can be found by elementary mathematics. The example we find is, apart from linear coordinate changes the example found by Le…
Kernels of linear maps: A generalization of Duistermaat and Van der Kallens theorem
Arno van den Essen, Jan Schoone
The theorem of Duistermaat and Van der Kallen from 1998 proved the first case of the Mathieu conjecture. Using the theory of Mathieu-Zhao spaces, we can reformulate this theorem as…
On the Image Conjecture for Locally Finite Derivations and -Derivations
Arno van den Essen, Wenhua Zhao
Some cases of the LFED Conjecture, proposed by the second author [Z3], for certain integral domains are proved. In particular, the LFED Conjecture is completely established for the…
The Gaussian Moments Conjecture and the Jacobian Conjecture
Harm Derksen, Arno van den Essen, Wenhua Zhao
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-exampl…
The Strong Factorial Conjecture
Eric Edo, Arno van den Essen
In this paper we present an unexpected link between the Factorial Conjecture and Furter's Rigidity Conjecture. The Factorial Conjecture in dimension asserts that if a polynomia…
Mathieu Subspaces of Univariate Polynomial Algebras
Arno van den Essen, Wenhua Zhao
We first give a characterization for Mathieu subspaces of univariate polynomial algebras over fields in terms of their radicals. We then deduce that for some classes of classical u…
On the Image Conjecture
Arno van den Essen, David Wright, Wenhua Zhao
The Image Conjecture was formulated by the third author, who showed that it implied his Vanishing Conjecture, which is equivalent to the famous Jacobian Conjecture. We prove variou…
The Amazing Image Conjecture
Arno van den Essen
In this paper we discuss a general framework in which we present a new conjecture, due to Wenhua Zhao, the Image Conjecture. This conjecture implies the Generalized Vanishing Conje…
Images of Locally Finite Derivations of Polynomial Algebras in Two Variables
Arno van den Essen, David Wright, Wenhua Zhao
In this paper we show that the image of any locally finite -derivation of the polynomial algebra in two variables over a field of characteristic zero is a Mathieu…
Unipotent group actions on affine varieties
Harm Derksen, Arno van den Essen, David R. Finston +1
Algebraic actions of unipotent groups actions on affine varieties ( an algebraically closed field of characteristic 0) for which the algebraic quotient has sm…
Some Results on the Vanishing Conjecture of Differential Operators with Constant Coefficients
Arno van den Essen, Roel Willems, Wenhua Zhao
In this paper we prove four cases of the vanishing conjecture of differential operators with constant coefficients and also a conjecture on the Laurent polynomials with no holomorp…
Stable Tameness of Two-Dimensional Polynomial Automorphisms Over a Regular Ring
Joost Berson, Arno van den Essen, David Wright
In this paper it is established that all two-dimensional polynomial automorphisms over a regular ring R are stably tame. In the case R is a Dedekind Q-algebra, some stronger result…
On ring homomorphisms of Azumaya algebras
Kossivi Adjamagbo, Jean-Yves Charbonnel, Arno Van Den Essen
The main theorem (Theorem 4.1) of this paper claims that any ring morphism from an Azumaya algebra of constant rank over a commutative ring to another one of the same constant rank…