Article citationsMore>>

Hardy, G.H. and Littlewood, J.E. (1917) Contributions to the Theory of the Riemann Zeta-Function and the Theory of the Distribution of Primes. Acta Mathematica, 41, 119-196.

has been cited by the following article:

• TITLE: All Zeros of the Riemann Zeta Function in the Critical Strip Are Located on the Critical Line and Are Simple

  AUTHORS: Frank Stenger

  KEYWORDS: Riemann Hypothesis, Fourier Transforms, Schwarz Reflection Principle, Cauchy-Riemann Equations, Trapezoidal-Midordinate Quadrature

  JOURNAL NAME: Advances in Pure Mathematics, Vol.13 No.6, June 29, 2023

  ABSTRACT: In this paper we study the function , for z∈C. We derive a functional equation that relates G(z) and G(1−z) for all z∈C, and we prove: 1) that G and the Riemann zeta function ζ have exactly the same zeros in the critical region D:= {z∈C:ℜz∈(0,1)}; 2) the Riemann hypothesis, i.e., that all of the zeros of G in D are located on the critical line := {z∈D:ℜz =1/2}; and that 3) all the zeros of the Riemann zeta function located on the critical line are simple.