A math course explaining the Riemann zeta function
Curated by: Zeta Explained (121 videos)
This is the 97th 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. Sources Graham & Kolesnik, "Van der Corput's Method of Exponential Sums" Ivić, "The Riemann Zeta-Function: Theory and Applications" This particular video discusses the theory of two-dimensional exponential sums, which were historically used to bound the growth rate of the zeta function below Phillips's 1933 result of 0.16451, eventually getting down to Kolesnik's 1985 bound of 0.16200. 00:00 - Intro and the Lindelöf Hypothesis 02:00 - The double sum from the A process 04:08 - Graphs of 1D and 2D exponential sums 08:14 - Exponent pairs and exponent quadruples 13:33 - Final table of results