Zeta (ζ) in LaTeX
\zeta typesets the lowercase Greek letter zeta (ζ) in maths mode; it has no distinct uppercase form in LaTeX, since capital zeta looks identical to a Latin Z.
LaTeX command
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Zeta's single most famous use is the Riemann zeta function, \zeta(s), defined for complex s as an infinite sum where it converges and extended elsewhere by analytic continuation; the still-unproven Riemann hypothesis is a statement about where its non-trivial zeros lie.
Outside number theory, zeta shows up as a damping ratio in control theory and mechanical vibrations, describing how quickly an oscillating system settles, and occasionally as a general-purpose variable name for an angle or a complex parameter once alpha, beta, gamma and delta have already been used up in the same problem.
As with alpha and beta, there is no \Zeta command since uppercase zeta is visually indistinguishable from the Latin letter Z; if a document genuinely needs an uppercase zeta it is simply typed as Z.
Other forms
\zetalowercase zetaExamples
$\zeta$lowercase zeta inline
$\zeta(s) = \sum_{n=1}^{\infty} \dfrac{1}{n^s}$the Riemann zeta function
$\zeta(2) = \dfrac{\pi^2}{6}$a famous special value, the Basel problem
$0 < \zeta < 1$the underdamped range for a damping ratio
Tips and common mistakes
- There is no
\Zetacommand, an uppercase zeta is just typed as a plain Latin Z, the glyphs are identical. \zeta(s) with a function-style argument almost always means the Riemann zeta function in a number-theory context, make surrounding text clarify the meaning if you're using zeta for something else nearby.- In control theory and vibrations, zeta as a damping ratio is a plain dimensionless number, typically written without an argument, don't confuse it with the zeta function's
\zeta(s) notation. \zetaneeds no extra package, it is built into core LaTeX.- If you've already used alpha through epsilon as generic placeholder variables in a problem, zeta is a natural next choice before resorting to Latin letters again.
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Convert your maths to LaTeX →FAQ
What is the LaTeX command for zeta?
\zeta, for example .
What is the Riemann zeta function?
Written \zeta(s), it is a function of a complex variable s defined by an infinite sum for Re(s) greater than 1 and extended by analytic continuation elsewhere; it is central to number theory and the unproven Riemann hypothesis.
Is there an uppercase zeta?
LaTeX has no \Zeta command, since capital zeta looks identical to the Latin letter Z, so you would just type Z if you needed it.
What does zeta mean in engineering?
Most commonly the damping ratio of a second-order system, a dimensionless number describing how oscillations decay: zeta less than 1 is underdamped, equal to 1 is critically damped, greater than 1 is overdamped.