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

Chang Lv; Junchao Shentu; Yingpu Deng

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arXiv · 1510.04800

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

Chang Lv·Junchao Shentu·Yingpu Deng

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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.

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BibTeX RIS

Chang Lv, Junchao Shentu, Yingpu Deng. 2016-12-06. On the Integral Representation of Binary Quadratic Forms and the Artin Condition. https://arxiv.org/abs/1510.04800

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