Zeta Explained Course

Currently Playing: Zeta Explained #29: Visualizing the Riemann Hypothesis

This is the 29th video in a series explaining the Riemann zeta function. The idea of the series is to start with basics and eventually work our way to advanced topics. The viewer is expected to understand calculus and complex numbers, whereas I will try to explain concepts from complex analysis as needed. We will follow the books "The Riemann Zeta Function: Theory and Applications" by Aleksandar Ivić and "Riemann's Zeta Function" by H. M. Edwards. This particular video discusses how to visualize the Riemann Zeta function on the critical line, what the Riemann Hypothesis is, what the Riemann–Siegel Z function is, and what the Z function should look like if the Riemann Hypothesis is true or false. Nearly all the math content in the video is from the book "Riemann's Zeta Function" by H. M. Edwards. 00:00 - Intro 02:54 - Basic Visualization 12:59 - Visualzing the Z function (Riemann–Siegel Z function) 16:27 - Gram Points 20:34 - Gram's Law 26:36 - Checking the Riemann Hypothesis 31:01 - Visualizing a hypothetical failure of the Riemann Hypothesis 40:30 - Lehmer's Phenomenon 44:09 - Table of progress computationally verifying Riemann Hypothesis 45:31 - Final graph of zeta function