Notes on the Zeros of Riemann's Zeta Function

2009/11/06 by Milgram, Michael S.
#11M26 #FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.0911.1332

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 ζ(s) will only occur on the critical line σ=1/2 where s=σ+I ρ, 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 ζ(s) on the critical line.

Related

• An investigation of the non-trivial zeros of the Riemann zeta function
• Constructing a Proof of the Riemann Hypothesis
• All of zeros of Riemann's Zeta-Function are on σ=1/2
• Arguments Related to the Riemann Hypothesis: New Methods and Results
• Zeros of the Riemann Zeta Function