School Seminars and Colloquia

Crouching AGM, Hidden Modularity


by Wadim Zudilin

Institution: The University of Newcastle
Date: Tue 11th April 2017
Time: 12:00 PM
Location: Russell Love Theatre

Abstract: Special arithmetic series, whose Taylor coefficients are usually defined as certain binomial sums, satisfy "self-replicating" functional identities. In my talk I will highlight the modular-function origin of such identities and discuss applications of the equations that do not make use of the modularity. In particular, I will outline an elementary recipe of generating AGM-type (aka Brent-Salamin) algorithms for computing $\pi$ and other related constants.

The talk is based on joint work with Shaun Cooper, Jes\'us Guillera and Armin Straub, and is dedicated to the memory of Jon Borwein.

Colloquium Website