NEW PROOFS FOR THE ABHYANKAR-GURJAR INVERSION FORMULA AND THE EQUIVALENCE OF THE JACOBIAN CONJECTURE AND THE VANISHING CONJECTURE

作者：Zhao Wenhua^*

来源：Proceedings of the American Mathematical Society, 2011, 139(9): 3141-3154.

DOI：10.1090/S0002-9939-2011-10744-5

• The Abhyankar-Gurjar inversion formula
• the Jacobian conjecture
• the vanishing conjecture of quadratic differential operators

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.

• 出版日期2011-9