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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

References (16)

  1. 1 The Theory of the Riemann Zeta-Function
  2. 2 Introduction to Analytic Number Theory [DOI]
  3. 3 The theory of functions
  4. 4 Complex Analysis
  5. 5 Multiplicative Number Theory [DOI]
  6. 6 Introduction to Analytic Number Theory [DOI]
  7. 7 The Riemann Zeta Function [DOI]
  8. 8 Complex Variables and Applications [DOI]
  9. 9 MULTIPLICATIVE NUMBER THEORY [DOI]
  10. 10 The Mellin Transform [DOI]
  11. 11 Lectures on the Riemann Zeta Function [DOI]
  12. 12 Introduction to the Gamma Function
  13. 13 Lectures on the Riemann zeta-function
  14. 14 The Distribution of Prime Numbers [DOI]
  15. 15 On the critical strip of the Riemann zeta-function
  16. 16 On the Theory of Zeta-functions and L-functions

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