ABC implies the radicalized Vojta height inequality for curves

[摘要] The truncated or radicalized counting function of a meromorphic function f:C -> P-1(C) 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 Vojta's height inequality for curves, J. Number Theory 95 (2002) 289-302], we prove the radicalized version of Vojta's height inequality, using the ABC conjecture. We explain the connection with a conjecture of Serge Lang about the different error terms associated with Vojta's height inequality and with the radicalized Vojta height inequality. (c) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-12-01

[关键词] ABC conjecture;the error term in the ABC conjecture;radicalized Vojta height inequality;Diophantine approximation;Roth's theorem;type of an algebraic number;Mordell's conjecture;effective Mordell