Definition:P-adic Expansion
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Definition
Let $p$ be a prime number.
A $p$-adic expansion is a series in the rational numbers $\Q$ of the form:
- $\ds \sum_{n \mathop = m}^\infty d_n p^n$
where:
- $m \in \Z_{\le 0}$
- $\forall n \in \Z_{\ge m}: d_n$ is a $p$-adic digit
- $m < 0 \implies d_m \ne 0$
Also see
Sources
- 1997: Fernando Q. Gouvea: p-adic Numbers: An Introduction ... (previous) ... (next): $\S 3.3$ Exploring $\Q_p$
- 2007: Svetlana Katok: p-adic Analysis Compared with Real ... (previous) ... (next): $\S 1.4$ The field of $p$-adic numbers $\Q_p$