Algebraic Number Theory
《Algebraic Number Theory》 · 第 101 页 · Chapter II，Section 1「The p-adic Numbers」
In analogy with the Laurent series $f(z)=\sum_{\nu=-m}^{\infty}a_\nu(z-a)^\nu$, we now extend the domain of $p$-adic integers into that of the formal series $\sum_{\nu=-m}^{\infty}a_\nu p^\nu=a_{-m}p^{-m}+\cdots+a_{-1}p^{-1}+a_0+a_1p+\cdots$, where $m\in\mathbb Z$ and $0\leq a_\nu<p$. Such series we call simply $p$-adic numbers and we write $\mathbb Q_p$ for the set of all these $p$-adic numbers.