Zeta Explained Course

Currently Playing: Zeta Explained #62: The Cosine Sum on the Critical Line

This is the 62nd 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. We follow the text "The Riemann Zeta-Function: Theory and Applications" by Aleksandar Ivić. This particular video covers how to turn the Hardy–Littlewood Approximate Functional Equation into a cosine sum that can be used to approximate the Z function. Note the Z function is referred to as both the Riemann–Siegel Z function and the Hardy Z function. 00:00 - Background 04:59 - The cosine sum 06:52 - Proof part 1: a lemma 13:54 - Proof part 2: the cosine sum 20:16 - Graph of the approximation 24:14 - The Riemann–Siegel formula