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.