Zeta Explained Course

Currently Playing: Zeta Explained #96: The A and B Processes on Exponent Pairs

This is the 96th 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 Titchmarsh, "The Theory of the Riemann Zeta-Function". https://sites.math.rutgers.edu/~zeilberg/EM18/TitchmarshZeta.pdf Ivić, "The Riemann Zeta-Function: Theory and Applications" Graham & Kolesnik, "Van der Corput's Method of Exponential Sums" This particular video discusses the math behind formulas on exponent pairs corresponding tovan der Corput's A and B processes. Specifically, we "prove" heuristically that if (p,q) is an exponent pair, then the following are also exponent pairs: A(p,q) = (p/(2p+2), 1/2+q/(2p+2)) B(p,q) = (q-1/2, p+1/2) 00:00 - Intro 02:31 - A process proof 08:49 - B process proof