A math course explaining the Riemann zeta function
Curated by: Zeta Explained (121 videos)
This is the 40th 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 first proof of the functional equation for the zeta function, using the global function covered in Episode 39. Riemann's 1859 paper here: https://www.claymath.org/wp-content/uploads/2023/04/Wilkins-translation.pdf 00:00 - Intro and review of Riemann's global equation (integral formula) 05:55 - Start of the functional equation paragraph 07:12 - Riemann's contour 14:42 - The Residue theorem and the C_N integral 25:30 - Equating the C_N and H_N terms to get the functional equation 26:45 - The S_N term vanishes 32:09 - Final remarks