Zeta in LaTeX (\zeta)

Where it is used

Lowercase Greek zeta, best known for the Riemann zeta function and the damping ratio.

The Riemann zeta function \zeta(s) = \sum_{n=1}^{\infty} n^{-s} is the signature use, with the Basel result \zeta(2) = \pi^2/6. Engineers use \zeta as the damping ratio of a second-order system, as in \ddot{x} + 2\zeta\omega_n \dot{x} + \omega_n^2 x = 0. Complex analysis uses it for a dummy complex variable, and number theory for roots of unity \zeta_n = e^{2\pi i/n}. There is no \Zeta command because capital zeta equals Latin Z. Its handwritten form is easily confused with \xi, so check which letter a source intends.

Minimal compilable example

Paste this into an empty .tex file and compile it with pdfLaTeX, XeLaTeX or LuaLaTeX.

\documentclass{article}
\begin{document}
Zeta: $\zeta$

\[ \zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s}, \quad \zeta(2) = \frac{\pi^2}{6} \]
\end{document}

Related symbols

• Eta\eta
• Epsilon (Variant)\varepsilon
• Theta\theta
• Epsilon\epsilon
• Theta (Upper)\Theta
• Delta (Upper)\Delta

Frequently asked questions

How do I write Zeta in LaTeX?

Type \zeta in math mode, for example $\zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s}, \quad \zeta(2) = \frac{\pi^2}{6}$. It works in plain LaTeX without loading any package.

Which package do I need for \zeta?

None. \zeta is part of standard LaTeX, so it compiles with nothing in the preamble but the document class.

Can I use \zeta in text mode, or only in math mode?

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\zeta$ in running text. If you only need the glyph in text, paste the Unicode character ζ instead (with XeLaTeX or LuaLaTeX and a font that has it).