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Research Article Open access CC BY 4.0

The Riemann Zeta Function and Its Analytic Continuation

Alhadbani Ahlam, Fredrik Stromberg

Journal of Advances in Mathematics and Computer Science · pp. 1–47 · Published 7 Jun 2017

10.9734/BJMCS/2017/32796

Abstract

The objective of this dissertation is to study the Riemann zeta function in particular it will examine its analytic continuation, functional equation and applications. We will begin with some historical background, then define of the zeta function and some important tools which lead to the functional equation. We will present four different proofs of the functional equation. In addition, the ζ(s) has generalizations, and one of these the Dirichlet L-function will be presented. Finally, the zeros of ζ(s) will be studied.

Riemann zeta function zeros of zeta function Dirichlet L-function

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