The Riemann Zeta Function
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In order to make progress in number theory, it is sometimes necessary to use techniques from other areas of mathematics, such as algebra, analysis or geometry. In this chapter we give some number-theoretic applications of the theory of infinite series. These are based on the properties of the Riemann zeta function ς(s), which provides a link between number theory and real and complex analysis. Some of the results we obtain have probabilistic interpretations in terms of random integers. For the background on convergence of infinite series, see Appendix C. For a detailed treatment of ς(s), see Titchmarsh (1951).
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