Crouching AGM, Hidden Modularity
by Wadim Zudilin
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.