Abstract
THE function now known as Riemann's zeta-function may be defined as the sum of the sth powers of the reciprocals of all the positive integers from unity to infinity. This definition only holds for a certain range of values of s, but it may be generalised, in the usual way, by contour integration. So far back as 1737, Euler had noticed the relation between this function and an infinite product involving primes. No further progress seems to have been made until 1859, when Riemann, in a short paper of only ten pages, indicated a number of ideas which have proved extraordinarily fruitful, and from which many modern researches have developed.
The Zeta-Function of Riemann.
Prof. E. C. Titchmarsh. (Cambridge Tracts in Mathematics and Mathematical Physics, No. 26.) Pp. vi + 104. (Cambridge: At the University Press, 1930.) 6s. 6d. net.
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P., H. The Zeta-Function of Riemann . Nature 126, 600 (1930). https://doi.org/10.1038/126600c0
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DOI: https://doi.org/10.1038/126600c0