Some Remarks on the Jacobian Conjecture and Connections with Hilbert’s Irreducibility Theorem
نویسندگان
چکیده
We have two main results. 1. Let P : Kn → Kn be a polynomial map with constant nonzero Jacobian, where K is any extension of Q. Then, P has a polynomial inverse if and only if the range of P contains a cartesian product of n universal Hilbert sets. 2. Let P : K → K be a polynomial map with constant nonzero Jacobian, where K is an algebraic number field. Then, P is invertible for “almost all” rational integers over K.
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تاریخ انتشار 2005