Abstract
For diophantine equations of the form $ax^2+bxy+cy^2+g=0$ over $\mathbb{Z}$ whose coefficients satisfy some assumptions, 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.
Citation
Yingpu DENG. Chang LV. Junchao SHENTU. "On the Integral Representation of Binary Quadratic Forms and the Artin Condition." Tokyo J. Math. 41 (2) 371 - 384, December 2018. https://doi.org/10.3836/tjm/1502179249
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