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

Chang Lv, Junchao Shentu

Given a number field $F$ with ${ø}_F$ its ring of integers. For certain $a,b$ and $\alpha$ in ${ø}_F$, we show that the Artin condition is the only obstruction to the local-global principle…