Zeta Explained Course

Currently Playing: Zeta Explained #74: Titchmarsh's Proof of Infinitely Many Zeros on Critical Line

This is the 74th 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 an alternate proof of Hardy's theorem that there are infinitely many zeros on the critical line. The alternate proof is by Titchmarsh, who analyzes Z(t) at Gram points using the Riemann–Siegel formula. 00:00 - Intro and background 04:06 - Proof outline 08:12 - Start of proof 15:00 - Rigorously proving that the cosine sum does not grow too large 21:17 - Finishing the proof 22:40 - Comparing proofs of Hardy vs Titchmarsh 25:16 - Outro Video covering Hardy's earlier proof (1914): https://www.youtube.com/watch?v=uyJ_a55SSuM