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The LaTeX command for zeta (ζ) is \zeta.
\zetaWrite \zeta inside math mode — that is, between $…$ for inline math or in a \[ … \] / equation block for display math. It is part of core LaTeX math, so no extra package is required.
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Use \zeta in math mode — it needs no extra package. For example, $\zeta \in \mathbb{R}$.
None — \zeta is built into LaTeX's math mode, so no extra package is required.