On the Integral Representation of Binary Quadratic Forms and the Artin Condition

Abstract

For diophantine equations of the form ax^2+bxy+cy^2+g=0 over Z whose coefficients satisfy some assumptions, we show that a condition with respect to 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.

11 pages, git commit 20150803a/3b8df3d. arXiv admin note: substantial text overlap with arXiv:1502.07457

References in corpus (1)

• On the Integral Representation of $a{x}^2+b{y}^2$ and the Artin Condition