In this paper E. Formanek says: ``The purpose of this paper is to point out a connection between certain differential equations which have arisen in attempts to establish the two-variable Jacobian Conjecture and the work of W. W. Stothers on the polynomial abc-conjecture".
Formanek applies results of T.-T. Moh and S. S. Abhyankar.
Is there any progress in the above direction? Moreover, are there other known connections between the (two-dimensional) Jacobian Conjecture and other number theory results/conjectures?
This question is relevant.
Thank you very much!