A short account of the values of the zeta function at integers

Huxley, Martin Neil 2018. A short account of the values of the zeta function at integers. Functiones et Approximatio Commentarii Mathematici 58 (2) , pp. 245-256. 10.7169/facm/1701

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Abstract

We use methods of real analysis to continue the Riemann zeta function ζ(s)ζ(s) to all complex ss, and to express the values at integers in terms of Bernoulli numbers, using only those infinite series for which we could write down an explicit estimate for the remainder after NN terms. This paper is self-contained, apart from appeals to the uniqueness theorems for analytic continuation and for real power series, and, verbis in Latinam translatis, would be accessible to Euler.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Faculty of Mathematics and Computer Science of Adam Mickiewicz University
ISSN:	0208-6573
Last Modified:	22 Oct 2018 13:52
URI:	https://orca.cardiff.ac.uk/id/eprint/107714

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