zeta function, n.

zeta-function
http://www.oed.com/dictionary/zeta-function_n%3Ftab%3Dmeaning_and_use
Revised 2018

# zeta functionnoun

## Factsheet

### What does the noun zeta function mean?

There are two meanings listed in OED's entry for the noun zeta function. See ‘Meaning & use’ for definitions, usage, and quotation evidence.

### How common is the noun zeta function?

About 0.03occurrences per million words in modern written English

1900 | 0.0014
1910 | 0.0017
1920 | 0.0025
1930 | 0.0036
1940 | 0.0053
1950 | 0.0081
1960 | 0.013
1970 | 0.02
1980 | 0.027
1990 | 0.03
2000 | 0.034
2010 | 0.04

### Where does the noun zeta function come from?

Earliest known use

1870s

The earliest known use of the noun zeta function is in the 1870s.

OED's earliest evidence for zeta function is from 1879, in Proceedings of Royal Society.

### Nearby entries

1. zest, v. 1702–
2. zest, int. 1705–22
3. zester, n. 1963–
4. zestful, adj. 1797–
5. zestfully, adv. 1843–
6. zestiness, n. 1912–
7. zesty, adj. 1826–
8. zeta, n.¹?a1425–
9. zeta, n.² 1706–1860
10. zetacism, n. 1860–
11. zeta function, n.1879–
12. zeta-ic, adj. 1840–1927
13. zeta potential, n. 1927–
14. zetetic, adj. & n. 1645–
15. zetetical, adj. & n. 1646–
16. zetetically, adv. 1665–
17. Zetetical Society, n. 1881–
18. zetetics, n. 1843–
19. Zetland, n. 1577–
20. Zetlander, n. 1614–
21. Zetlandic, adj. 1701–

## Meaning & use

Mathematics.

1. 1879–
   a. Any member of several families of functions connected with elliptic integrals, typically denoted by ‘Z’ or ‘ζ’; b. the Riemann zeta function; (in later use also) any of various functions generalizing the Riemann zeta function to a different context or otherwise regarded as somehow analogous to it.
   Frequently with modifying word.
   1. 1879

      > ‘Values of the Theta and Zeta Functions for certain Values of the Argument.’ By J. W. L. Glaisher.

      Proceedings of Royal Society vol. 29 351 (heading)
   2. 1901

      > The Double Riemann Zeta Function.

      Philosophical Transactions (Royal Society) A. vol. 196 266
   3. 1943

      > The second part of the paper is concerned with similar problems for certain Epstein zeta-functions.

      Annals of Mathematics vol. 44 144
   4. 1995

      > An antiderivative for the function..is given by the Weierstrass zeta function.

      American Math. Monthly vol. 102 432
   5. 2015

      > If we know enough about the zeros of the zeta function, we can deduce a lot of new information about the primes from Riemann's formula.

      I. Stewart, Professor Stewart's Incredible Numbers (Electronic edition)
   mathematics

## Frequency

zeta function typically occurs about 0.03 times per million words in modern written English.

zeta function is in frequency band 3, which contains words occurring between 0.01 and 0.1 times per million words in modern written English. More about OED's frequency bands

Frequency data is computed programmatically, and should be regarded as an estimate.

### Frequency of zeta function, n., 1900–2010

* Occurrences per million words in written English

Historical frequency series are derived from Google Books Ngrams (version 2), a data set based on the Google Books corpus of several million books printed in English between 1500 and 2010.

The overall frequency for a given word is calculated by summing frequencies for the main form of the word, any plural or inflected forms, and any major spelling variations.

For sets of homographs (distinct entries that share the same word-form, e.g. mole, n.¹, mole, n.², mole, n.³, etc.), we have estimated the frequency of each homograph entry as a fraction of the total Ngrams frequency for the word-form. This may result in inaccuracies.

Smoothing has been applied to series for lower-frequency words, using a moving-average algorithm. This reduces short-term fluctuations, which may be produced by variability in the content of the Google Books corpus.

Decade | Frequency per million words
--- | ---
1900 | 0.0014
1910 | 0.0017
1920 | 0.0025
1930 | 0.0036
1940 | 0.0053
1950 | 0.0081
1960 | 0.013
1970 | 0.02
1980 | 0.027
1990 | 0.03
2000 | 0.034
2010 | 0.04

Originally published as part of the entry for zeta, n.¹

zeta, n.¹ was revised in June 2018.