A math course explaining the Riemann zeta function
Curated by: Zeta Explained (121 videos)
This is the 66th 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 covers Section 7.8 of "Riemann's Zeta Function" by H.M. Edwards. He explains how Riemann might have been led to believe the Riemann Hypothesis due to the behavior of the Riemann-Siegel formula. We go over the math that Riemann carried out and what could have led him to the Riemann Hypothesis. 00:00 - Intro 01:54 - History 06:59 - The Riemann-Siegel Z and θ functions, and the Riemann-Siegel formula. 14:43 - Cosine heuristic of location of zeros 17:46 - The Riemann-von Mangoldt formula 22:46 - Visualization of the cosine heuristic (very similar to Gram points) 29:20 - Sample table of the first cosine term relative to other terms