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arXiv · 1502.07457

On the Integral Representation of $ax^2+by^2$ and the Artin Condition

Chang Lv·Junchao Shentu
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Abstract

Given a number field $F$ with $\o_F$ its ring of integers. For certain $a,b$ and $\alpha$ in $\o_F$, we show that the Artin condition is the only obstruction to the local-global principle for integral solutions of equation $ax^2+by^2=\alpha$. Some concrete examples are presented at last.

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Chang Lv, Junchao Shentu. 2015-02-26. On the Integral Representation of $ax^2+by^2$ and the Artin Condition. https://arxiv.org/abs/1502.07457

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