# Riemann zeta function

> English word · Noun

## Definitions
1. The function ζ defined by the Dirichlet series ζ(s)=∑ₙ₌₁ ᪲1/(nˢ)=1/(1ˢ)+1/(2ˢ)+1/(3ˢ)+1/(4ˢ)+⋯, which is summable for points s in the complex half-plane with real part > 1; the analytic continuation of said function, being a holomorphic function defined on the complex numbers with pole at 1.
2. A usage of (a specified value of) the Riemann zeta function, such as in an equation.

## Etymology
Named after German mathematician Bernhard Riemann.

## Source
Compiled from Wiktionary via kaikki.org (CC BY-SA). Data vintage: 2026-05-06.
Canonical page: https://plainspell.com/en/word/riemann-zeta-function