Open AccessThe Riemann Zeta Function and Its Zeroes
Author(s) -
Taghreed Hamdi Alhadbani
Publication year - 2022
Publication title -
current journal of applied science and technology
Language(s) - English
Resource type - Journals
ISSN - 2457-1024
DOI - 10.9734/cjast/2022/v41i431662
Subject(s) - riemann zeta function , riemann xi function , riemann hypothesis , particular values of riemann zeta function , mathematics , arithmetic zeta function , functional equation , dirichlet series , generalization , mathematical analysis , explicit formulae , prime zeta function , function (biology) , analytic continuation , pure mathematics , dirichlet distribution , partial differential equation , boundary value problem , evolutionary biology , biology
This dissertation includes a detailed of the Riemann zeta functions; with a particular focus its analytic continuation, functional equation and application. We will start with the historical background. Following this we cover certain important preliminaries which are needed to use the functional equation. We then define the Riemann zeta function and prove the functional equation. In addition to this that, we show the Riemann zeta function has generalization in form of the Dirichlet L-function. Then, the zeroes of the Riemann zeta function will be studied. Finally, we establish the zero free region of Riemann zeta function.