Diophantine equations defined by binary quadratic forms over rational function fields
Volume 196 / 2020
Acta Arithmetica 196 (2020), 35-51
MSC: Primary 11E12, 11D57, 11R58; Secondary 14L30, 11R37.
DOI: 10.4064/aa190404-8-12
Published online: 10 June 2020
Abstract
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 on the Artin reciprocity map is the only obstruction to the local-global principle for integral solutions of the equation.
