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table.yaml
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table.yaml
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ID: INPUT{id.yaml}
Title: >
Teichmüller representatives in $\mathbb{Z}_p$
Definition: >
Let $p$ be a rational prime,
let $q=p$ for $p>2$ and $q=4$ for $p=2$,
let $G = (\mathbb{Z}/q\mathbb{Z})^\times$,
and let $\omega: G \to \mathbb{Z}_p^*$ be
the Teichmüller character CITE{Wiki}.
The images $\omega(k)$ of elements $k \in G$ are their
Teichmüller representatives in $\mathbb{Z}_p$.
Parameters:
p:
type: Z
constraints: prime
k:
type: Z
constraints:
- >
$1 \leq k < p$ for $p>2$
- >
$k = \pm 1$ for $p=2$
Comments:
comment-roots-of-unity: >
The set of Teichmüller representatives in $\mathbb{Z}_p$
equals the set of non-zero roots of unity in $\mathbb{Z}_p$.
The $k$'th Teichmüller representative reduces to $k$ modulo $p$.
Formulas:
Programs:
References:
Links:
Wiki:
title: "Wikipedia: Teichmüller character"
url: https://en.wikipedia.org/wiki/Teichm%C3%BCller_character
Similar tables:
Keywords:
Tags:
- p-adic
- zero
Data properties:
type: Qp
complete: no
Display properties:
number-header: Teichmüller representative of $k$ in $\mathbb{Z}_p$
Numbers: INPUT{numbers.yaml}