---
type: Fractal Concept
title: Riemann Zeta Function
description: Complex analytic function zeta(s) = sum_{n≥1} 1/n^s, central to number theory; its non-trivial zeros lie (conjecturally) on the critical line Re(s) = 1/2.
resource: https://tyson-swetnam.github.io/fractal-notebooks/okf/concepts/number-theory/riemann-zeta-function/
tags:
- number-theory
- complex-analysis
- foundations
aliases:
- zeta function
- riemann zeta
sources:
- id: glossary
  resource: https://tyson-swetnam.github.io/fractal-notebooks/foundations/glossary/
  title: Fractal Notebooks glossary (Chapter 4)
- id: seed
  resource: https://github.com/tyson-swetnam/fractal-notebooks/blob/main/fractal_rag/src/fractal_rag/concepts/seed.yaml
  title: fractal_rag concept seed (seed.yaml)
generated:
  by: process:fractal-rag-okf-export
  at: "2026-10-24T00:00:00Z"
status: stable
---

# Definition

Complex analytic function zeta(s) = sum_{n>=1} 1/n^s, central to number theory; its non-trivial zeros lie (conjecturally) on the critical line Re(s) = 1/2.

# Aliases

`zeta function`, `riemann zeta`

# Citations

[1] [Fractal Notebooks glossary (Chapter 4)](https://tyson-swetnam.github.io/fractal-notebooks/foundations/glossary/) — `docs/foundations/glossary.md`

[2] [fractal_rag concept seed (seed.yaml)](https://github.com/tyson-swetnam/fractal-notebooks/blob/main/fractal_rag/src/fractal_rag/concepts/seed.yaml) — `fractal_rag/src/fractal_rag/concepts/seed.yaml`