Cartan's conjecture with moving targets of same growth and effective Wirsing's theorem over function fields
type: Item
instance of: scholarly article
title: Cartan's conjecture with moving targets of same growth and effective Wirsing's theorem over function fields
zbMATH Open document ID: 0971.11037
author: Julie Tzu-Yueh Wang
published in: Mathematische Zeitschrift
publication date: 2000-11-20T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 11J25
Mathematics Subject Classification ID: 11J97
Mathematics Subject Classification ID: 14H05
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 1515379
zbMATH Keywords: Schmidt's subspace theorem
zbMATH Keywords: Cartan conjecture
zbMATH Keywords: Nochka weights
zbMATH Keywords: Wirsing's theorem
zbMATH Keywords: moving targets
reviewed by: Paul Vojta
MaRDI profile type: Publication
DOI: 10.1007/S002090000098
description: scientific article; zbMATH DE number 1515379