Singular values, Ramanujan modular equations, and Landen transformations

: Vuorinen M.

: 1996

: Studia Mathematica

: 121

: 3

: 221

: 230

: 0039-3223

: http://api.elsevier.com/content/abstract/scopus_id:0030470638

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(r) recurrent in the theory of plane quasiconformal maps. Ramanujan's modular identities yield numerous new functional identities for φ(r) for various primes p.