riemann-hypothesis

A repository of resources on the Riemann Hypothesis

Introductory Videos:

• The Riemann Hypothesis, Explained

• Visualizing the Riemann zeta function and analytic continuation

• Riemann Hypothesis visualised

• The Riemann Zeta Function Visualised

Reading Material:

• Wolfram: The Riemann Hypothesis
• Digital Library of Mathematical Functions: Chapter 25 Zeta and Related Functions

Established Facts:

• Riemann Hypothesis simplified: All the non-trivial zeros of the Riemann Zeta function (Z) have Re(Z) = 1/2
• Non-trivial zeros of the Riemann Zeta function have their real part between 0 and 1, 0 < Re(Z) < 1
• The non-trivial zeros of the Riemann Zeta function Z1 and Z2 come in symetric pairs, with Im(Z1) = - Im(Z2)
• The Prime Number Theorem: The non-trivial zeros of the Riemann Zeta function can reconstruct the prime counting function
• The "encoding" of the distribution of prime numbers by the nontrivial zeros of the Riemann zeta function [common approach]