A math course explaining the Riemann zeta function
Curated by: Zeta Explained (121 videos)
This is the 18th 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. The viewer is expected to understand calculus and complex numbers, whereas I will try to explain concepts from complex analysis as needed. We will follow the book "The Riemann Zeta Function: Theory and Applications" by Aleksandar Ivić. This particular video covers the growth rates of examples of complex functions such as polynomials, exponentials, and trig functions. It also introduces Jensen's formula and Hadamard's concept of entire functions of finite order. 00:00 - Growth rates are tied to zeros 00:26 - Examples of polynomials, and their growth rates and zeros 02:59 - Exponential functions, and their growth rates and zeros 05:48 - Trig functions (are actually exponential functions), and their growth rates and zeros 10:20 - Graphing the growth rates of trig functions 14:39 - Table of functions with growth rates vs zeros 15:44 - Entire functions of finite order 18:31 - Jensen's formula 22:21 - Riemann's xi function