Zeta
Zeta (Ζ, ζ) is the sixth letter of the Greek alphabet. In maths ζ(s) is the Riemann zeta function, whose zeros are the subject of the Riemann hypothesis, one of the Clay Mathematics Institute’s unsolved Millennium Prize Problems.
How to read it
Zeta is said ZEE-tuh in Britain and ZAY-tuh in America (Cambridge Dictionary: /ˈziː.tə/ and /ˈzeɪ.t̬ə/). In Modern Greek ζήτα, which the University of Arizona’s guide writes “Zita”, stands for a z sound.
Also searched as: zeta letter, zeta symbol, ζ, Ζ.
Capital, small and look-alike forms
| Form | Character | Code point | Unicode name |
|---|---|---|---|
| Capital | Ζ | U+0396 | Greek capital letter zeta |
| Small | ζ | U+03B6 | Greek small letter zeta |
The capital Ζ looks the same as the Latin Z (Cambridge Dictionary gives the letter’s symbols as Z and ζ), but it has its own code point.
The Riemann zeta function
NIST’s Digital Library of Mathematical Functions defines ζ(s) as the sum 1 + 1/2ˢ + 1/3ˢ + … for values of s whose real part is greater than 1. Bernhard Riemann introduced the letter ζ for it, as early as 1857, and used it in his 1859 paper “Über die Anzahl der Primzahlen unter einer gegebenen Grösse”, on the number of primes below a given size (Jeff Miller, Earliest Uses of Various Mathematical Symbols). The Clay Mathematics Institute explains that Riemann saw the frequency of prime numbers is very closely related to how this function behaves. The Riemann hypothesis, from the same 1859 paper, says that all the “non-obvious” zeros of the zeta function are complex numbers with real part 1/2. Clay says it has been checked for the first 10,000,000,000,000 of them, and that a proof would shed light on many mysteries about how the primes are distributed. It is on Clay’s list of Millennium Prize Problems.
More greek letters
Browse symbols drawn with letters and numbers.
Sources
- Greek and Coptic: Range 0370–03FF (code chart), The Unicode Standard, Version 18.0, Unicode Consortium, Greek and Coptic, pp. 39–41
- zeta (Cambridge Dictionary entry), Cambridge Advanced Learner’s Dictionary & Thesaurus, Cambridge University Press, zeta, noun
- zeta (American Heritage Dictionary entry), The American Heritage Dictionary of the English Language, Fifth Edition, HarperCollins Publishers, zeta, n.
- Modern Greek Alphabet And Phonetics, University of Arizona, Center for Middle Eastern Studies, Letter table
- NIST Digital Library of Mathematical Functions §25.2: Riemann Zeta Function, Definition and Expansions, U.S. National Institute of Standards and Technology, 25.2.1
- Earliest Uses of Function Symbols, Jeff Miller, Earliest Uses of Various Mathematical Symbols, MacTutor History of Mathematics, University of St Andrews, Riemann's zeta function
- Riemann Hypothesis, The Millennium Prize Problems, Clay Mathematics Institute, Problem description
Last reviewed September 30, 2026 by Rory Hansen. How we research