Zeta Explained Course

Currently Playing: Zeta Explained #41: Riemann's Second Proof of the Functional Equation (via Jacobi Theta Functions)

This is the 41st 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 book "Riemann's Zeta Function" by H.M. Edwards. This particular video covers Riemann's second proof of the functional equation for the zeta function, using the functional equation of the Jacobi "theta" function ψ(x). Riemann's 1859 paper here: https://www.claymath.org/wp-content/uploads/2023/04/Wilkins-translation.pdf 00:00 - Intro 01:39 - Proof 14:17 - Justifying the interchange of sum and integral 18:14 - Jacobi theta function(s) 21:30 - Why multiple proofs