Zeta Explained Course

Currently Playing: Zeta Explained #58: The Riemann–Siegel Z and θ Functions

This is the 58th 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 "Riemann's Zeta Function" by H.M. Edwards. This particular video goes over both math and animations behind the Riemann–Siegel Z and θ. 00:00 - Refresher math on N(T) = L(T) + S(T) 07:53 - Animation 1: N(T) = L(T) + S(T) 10:02 - Animation 2: The spiral of ζ(1/2+it) 14:11 - Animation 3: The Z and θ functions 18:32 - Math on Z and θ 25:04 - Animation 4: Why θ and L are "the same" 29:12 - Animation 5: Gram points 32:21 - Summary of definitions and properties of θ and L