Shaun Cooper, Jesús Guillera, Armin Straub, Wadim Zudilin — Chapter 9 of the book: Frontiers in Orthogonal Polynomials and q-Series (World Scientific) — Editors: Z. Nashed and X. Li — 2018, Pages 169-187
Abstract
Special arithmetic series , whose coefficients are normally given as certain binomial sums, satisfy `self-replicating' functional identities. For example, the equation generates a modular form of weight 2 and level 7, when a related modular parametrization is properly chosen. In this note we investigate the potential of describing modular forms by such self-replicating equations as well as applications of the equations that do not make use of the modularity. In particular, we outline a new recipe of generating AGM-type algorithms for computing and other related constants. Finally, we indicate some possibilities to extend the functional equations to a two-variable setting.Download
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BibTeX
@article{crouching-agm-2018, author = {Shaun Cooper and Jes\'us Guillera and Armin Straub and Wadim Zudilin}, title = {Crouching {AGM}, Hidden Modularity}, journal = {Chapter 9 of the book: Frontiers in Orthogonal Polynomials and q-Series (World Scientific)}, year = {2018}, pages = {169--187}, doi = {10.1142/9789813228887_0009}, }