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Verification of the Jacobian Conjecture for -linear maps in two variables
Mario DeFranco
For any integer , we verify the Jacobian Conjecture for a -linear map in two variables. We prove that almost all the coefficients of the formal inverse are in the idea…
On the Jacobian Conjecture and ideal membership for degree -linear maps
Mario DeFranco
We consider polynomial maps, which we call degree -linear maps, that satisfy the Jacobian condition. We prove that certain infinite families of elements, which appear in the coe…
On Taylor series of zeros with general base function
Mario DeFranco
We prove a formula for the Taylor series coefficients of a zero of the sum of a complex-exponent polynomial and a base function which is a general holomorphic function with a simpl…
On Taylor series of zeros of complex-exponent polynomials
Mario DeFranco
We prove a factorization formula for the Taylor series coefficients of a zero of a polynomial as a function of the polynomial's coefficients. This result extends to more general fu…