Singular values, Ramanujan modular equations, and Landen transformations
Volume 121 / 1996
Studia Mathematica 121 (1996), 221-230
DOI: 10.4064/sm-121-3-221-230
Abstract
A new connection between geometric function theory and number theory is derived from Ramanujan's work on modular equations. This connection involves the function $φ_K(r)$ recurrent in the theory of plane quasiconformal maps. Ramanujan's modular identities yield numerous new functional identities for $φ_{1/p}(r)$ for various primes p.
