Integral representation of binary quadratic forms over rational function fields

Chang Lv

Published 2017-04-06Version 1

For diophantine equations of the form ax^2+bxy+cy^2+g=0 over k[t], the ring of integers of rational funtional fields, we show that a condition with respect to the Artin reciprocity map, which we call the Artin condition, is the only obstruction to the local-global principle for integral solutions of the equation. Some concrete examples are presented.