The Riemann Zeta Function and Its Analytic Continuation
Alhadbani Ahlam *
School of Mathematical Sciences, University of Nottingham, England.
Fredrik Stromberg
School of Mathematical Sciences, University of Nottingham, England
*Author to whom correspondence should be addressed.
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.
Keywords: Riemann, zeta function, zeros of zeta function, Dirichlet, L-function