New Proofs for the Abhyankar-Gurjar Inversion Formula and the Equivalence of the Jacobian Conjecture and the Vanishing Conjecture

Abstract

We first give a new proof and also a new formulation for the Abhyankar-Gurjar inversion formula for formal maps of affine spaces. We then use the reformulated Abhyankar-Gurjar formula to give a more straightforward proof for the equivalence of the Jacobian Conjecture with a special case of the Vanishing Conjecture of (homogeneous) quadratic differential operators with constant coefficients.

arXiv commentLatex, 18 pages. Following the referee the Introduction and the preliminary part of the paper have been slightly re-written. To appear in Proc. AMS

References in corpus (3)

• A Vanishing Conjecture on Differential Operators with Constant Coefficients
• Some Results on the Vanishing Conjecture of Differential Operators with Constant Coefficients
• Two Results on Homogeneous Hessian Nilpotent Polynomials

Cited by in corpus (2)

• Mathieu Subspaces of Associative Algebras
• A Deformation of Commutative Polynomial Algebras in Even Numbers of Variables