Zeta Explained Course

Currently Playing: Zeta Explained #73: The Riemann–Siegel Formula via Saddle-Point Method

This is the 73rd 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 texts "The Riemann Zeta-Function" by Aleksandar Ivić and "Riemann's Zeta Function" by H.M. Edwards. This particular video goes over a powerful formula known as the Riemann–Siegel Formula. We continue the proof from Episodes 61-62, but continue to examine the error term, and prove the first error term, in addition to the main cosine sum which was already proved in 61-62. 00:00 - Intro and background 02:06 - Review of proof of main cosine sum 16:45 - New content 20:46 - The true saddle point 32:50 - The approximate saddle point 37:30 - Lots of cancellation 47:16 - Dealing with the integral 55:38 - The Riemann–Siegel Formula with one error term 58:22 - The full Riemann–Siegel Formula 59:53 - Review of computation of zeta from Ep 65