Cartan's conjecture with moving targets of same growth and effective Wirsing's theorem over function fields
Over function fields of dimension one and of characteristic zero, this paper proves analogues of Schmidt's Subspace Theorem, Cartan's conjecture (proved by Nochka), and Wirsing's theorem. These theorems, of course, are well known, but what is new here is that the theorems are proved with effectively computable constants instead of just bounds on the number of exceptions. The proof stems from an elegant proof of Nevanlinna's Second Main Theorem with moving targets originally given by \textit{N. Steinmetz} [J. Reine Angew. Math. 368, 134-141 (1986; Zbl 0598.30045)], and further improved by M. Ru, M. Shirosaki, the author, and the reviewer. The reference to ``moving targets of same growth'' in the title should perhaps be explained a bit more. It refers to the fact that the coefficients of the linear forms are allowed to be any elements of the function field, as opposed to elements of the constant subfield. The coefficients of the linear forms are not allowed to vary depending on the point, which is another interpretation of ``moving targets'' used by other authors.
scientific article; zbMATH DE number 1515379