Abstract :
We formulate some results of function fields which are analogous to Cartanʹs Second Main Theorem with truncated counting functions, Cartanʹs conjecture, and the generalized Picard Theorem. We also give a generalization of function fields version ofabc-conjecture due to Mason, Voloch, Brownawell, and Masser. A result of the finiteness of theS-integral points of function fields of characteristic 0 in the complement of 2n+1 hyperplanes with constant coefficients and in general position is obtained in this paper.
