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The Jacobian conjecture in two variables

โœ Scribed by Harry Appelgate; Hironori Onishi


Publisher
Elsevier Science
Year
1985
Tongue
English
Weight
657 KB
Volume
37
Category
Article
ISSN
0022-4049

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Let a, b # Q\* be rational numbers that are multiplicatively independent. We study the natural density $(a, b) of the set of primes p for which the subgroup of F p \* generated by (a mod p) contains (b mod p). It is shown that, under assumption of the generalized Riemann hypothesis, the density $(a,

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We prove that a polynomial map from \(\mathbf{R}^{n}\) to itself with non-zero constant Jacobian determinant is a stably tame automorphism if its linear part is the identity and all the coefficients of its higher order terms are non-positive. We also prove that the Jacobian conjecture holds for any