ABC implies the radicalized Vojta height inequality for curves Original Research Article

The truncated or radicalized counting function of a meromorphic function image counts the number of times that f takes a value a, but without multiplicity. By analogy, one also defines this function for numbers. In this sequel to [M. van Frankenhuijsen, The ABC conjecture implies Vojtaʹs height inequality for curves, J. Number Theory 95 (2002) 289–302], we prove the radicalized version of Vojtaʹs height inequality, using the ABC conjecture. We explain the connection with a conjecture of Serge Lang about the different error terms associated with Vojtaʹs height inequality and with the radicalized Vojta height inequality.