Zeta Explained Course

Currently Playing: Zeta Explained #60: Hardy's Proof of Infinitely Many Zeros on Critical Line

This is the 60th 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. This particular video covers a proof by Hardy in 1914 that there are infinitely many zeros on the critical line. This statement is also known as Hardy's Theorem. 00:00 - Intro 02:46 - Proof sketch and toy model 07:09 - Part 1: Definition and properties of Xi 10:25 - Part 2: The integral I(α) 14:37 - Part 3: The integral converges 21:35 - Part 4: The integral diverges 31:11 - The contradiction