Zeta Explained Course

Currently Playing: Zeta Explained #90: Weyl Differencing

This is the 90th 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 "The Theory of the Riemann Zeta-Function" by E.C. Titchmarsh. https://sites.math.rutgers.edu/~zeilberg/EM18/TitchmarshZeta.pdf This particular video covers two lemmas on exponential sums: Part 1 (Lemma 5.3 of Titchmarsh's text): Convert an exponential sum with log to an exponential sum with a quadratic for a short-enough interval Part 2 (Lemma 5.4 of Titchmarsh's text): Convert an exponential sum with a quadratic to a sum involving cosecants. 00:00 - Intro and background 05:30 - Part 1: Lemma 5.3 17:33 - Visualization of Part 1 22:19 - Part 2: Lemma 5.4 34:09 - General Weyl Differencing