$$\prod_{\mathfrak{p} \in \Omega}(\frac{\alpha,-1}{\mathfrak{p}})=1,$$

$$(X,\beta) \oplus (X,-\beta) \text{ is split }$$

$$ \sum_{n=1}^\infty \dfrac{f(n)}{n^s}=\prod_{p=\text{prime}} \dfrac{1}{1-f(p)p^{-s}} $$