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British Journal of Mathematics & Computer Science, ISSN: 2231-0851,Vol.: 22, Issue.: 5


The Riemann Zeta Function and Its Analytic Continuation


Alhadbani Ahlam1* and Fredrik Stromberg1
1School of Mathematical Sciences, University of Nottingham, England.

Article Information
(1) Mohd Zuki Salleh, Universiti Malaysia Pahang, Malaysia.
(1) Michael M. Anthony, Enertron Corp., Hohenwald, USA.
(2) Teodor Bulboaca, Babe-Bolyai University, Romania.
(3) Daniele Lattanzi, Frascati Research Centre, Roma, Italy.
Complete Peer review History: http://www.sciencedomain.org/review-history/19381


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.

Keywords :

Riemann; zeta function; zeros of zeta function; Dirichlet; L-function.

Full Article - PDF    Page 1-47 Article Metrics

DOI : 10.9734/BJMCS/2017/32796

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