---
date: 2022-04-05 23:42
modification date: Saturday 30th April 2022 21:19:29
title: "Dedekind zeta function"
aliases: [Dedekind zeta function]
---

Last modified date: <%+ tp.file.last_modified_date() %>

---

- Tags: 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- [class number](class%20number)
	- [regulator](regulator.md)

---

# Dedekind zeta function

For $K\in \NF$, defined as
$$
\zeta_K(s) \da \sum_{p\in \abs{\spec \OO_K}}{1\over 1 - \Norm_{K\slice \QQ}(p)} = \prod_{a\in \Id(\OO_K)} \qty{\Norm_{K\slice \QQ}(a)}^{-s}
$$
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# Completion

![](attachments/Pasted%20image%2020220430213421.png)

![](attachments/Pasted%20image%2020220126155814.png)

![](attachments/Pasted%20image%2020220126160009.png)
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