Geodesic
Singular values, Ramanujan modular equations, and Landen transformations
Studia Mathematica, Tome 121 (1996) no. 3, pp. 221-230 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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. 
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     title = {Singular values, {Ramanujan} modular equations, and {Landen} transformations},
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M. Vuorinen. Singular values, Ramanujan modular equations, and Landen transformations. Studia Mathematica, Tome 121 (1996) no. 3, pp. 221-230. doi: 10.4064/sm-121-3-221-230

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