Singular values, Ramanujan modular equations, and Landen transformations

M. Vuorinen

Studia Mathematica (1996)

  • Volume: 121, Issue: 3, page 221-230
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Vuorinen, M.. "Singular values, Ramanujan modular equations, and Landen transformations." Studia Mathematica 121.3 (1996): 221-230. <http://eudml.org/doc/216353>.

@article{Vuorinen1996,
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.},
author = {Vuorinen, M.},
journal = {Studia Mathematica},
keywords = {plane quasiconformal maps; modulus of Grötzsch domain; complete elliptic integral; Landen transformation},
language = {eng},
number = {3},
pages = {221-230},
title = {Singular values, Ramanujan modular equations, and Landen transformations},
url = {http://eudml.org/doc/216353},
volume = {121},
year = {1996},
}

TY - JOUR
AU - Vuorinen, M.
TI - Singular values, Ramanujan modular equations, and Landen transformations
JO - Studia Mathematica
PY - 1996
VL - 121
IS - 3
SP - 221
EP - 230
AB - 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.
LA - eng
KW - plane quasiconformal maps; modulus of Grötzsch domain; complete elliptic integral; Landen transformation
UR - http://eudml.org/doc/216353
ER -

References

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