Diophantine equations over global function fields II: R-integral solutions of Thue equations

摘要

Let K be an algebraic function field over a finite field. Let L be an extension field of K of degree at least 3. Let R be a finite set of valuations of K and denote by S the set of extensions of valuations of R to L. Denote by O-K,O-R O-L,O-S the ring of R-integers of K and S-integers of L, respectively. Assume that alpha is an element of O-L,O-S with L = K(alpha), let 0 not equal mu is an element of O-K,O-R, and consider the solutions (x, y) is an element of O-K,O-R of the Thue equation