A math course explaining the Riemann zeta function
Curated by: Zeta Explained (121 videos)
This is the 63rd 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 "Riemann's Zeta Function" by H.M. Edwards. This particular video goes over a powerful formula called the Riemann–Siegel Formula. We briefly discuss the history--how Riemann had a secret formula lost to the ages until it was rediscovered by Siegel in 1932. Then we go through visualizations and some of the "basic" math behind it. 00:00 - Intro and background 05:23 - History of the Riemann-Siegel formula 07:28 - Visualization of the main cosine sum and the error term 09:24 - Riemann-Siegel with one error term 12:18 - Riemann-Siegel, full equation 15:48 - More visualizations, including Lehmer phenomenon at t≈17143 19:37 - Proof of why the jump discontinuities seem to disappear when adding the first error term