Diophantine equations defined by binary quadratic forms over rational function fields

We study the ``imaginary" binary quadratic form equations ax^2+bxy+cy^2+g=0 over k[t] in rational function fields, showing that a condition with respect to the Artin reciprocity map, is the only obstruction to the local-global principle for integral solutions of the equation.Comment: 14 pages, git commit 20170117/57d58b6, to appear in Acta Arithmetic