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.
1879
‘Values of the Theta and Zeta Functions for certain Values of the Argument.’ By J. W. L. Glaisher.
Proceedings of Royal Societyvol. 29 351 (heading)
1901
The Double Riemann Zeta Function.
Philosophical Transactions (Royal Society) A. vol. 196 266
1943
The second part of the paper is concerned with similar problems for certain Epstein zeta-functions.
Annals of Mathematicsvol. 44 144
1995
An antiderivative for the function..is given by the Weierstrass zeta function.
American Math. Monthlyvol. 102 432
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)
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