Notes on the Zeros of Riemann's Zeta Function

Abstract

The functional equation for Riemann's Zeta function is studied, from which it is shown why all of the non-trivial, full-zeros of the Zeta function $\zeta (s)$ will only occur on the critical line {$\sigma =1/2$} where {$s=\sigma +I\rho$}, thereby establishing the truth of Riemann's hypothesis. Further, two relatively simple transcendental equations are obtained; the numerical solution of these equations locates all of the zeros of {$\zeta (s)$} on the critical line.

Corrections added July 30, 2015

References in corpus (2)

• On the Quantum Reconstruction of the Riemann zeros
• Large Spaces Between the Zeros of the Riemann Zeta-Function

Cited by in corpus (1)

• Exploring Riemann's Functional Equation