Singular values, Ramanujan modular equations, and Landen transformations

• Autorzy: M. Vuorinen
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 30C62: Quasiconformal mappings in the plane
• 33C55: Spherical harmonics

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1996
• Tom: 121
• Numer: 3
• Strony: 221-230

Daty

wydano

1996

otrzymano

1995-03-20

poprawiono

1996-09-11

Twórcy

autor

M. Vuorinen

• Department of Mathematics, University of Helsinki, P.O. Box 4 (Yliopistonk. 5), FIN-00014 Helsinki, Finland

Bibliografia

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• [VV] M. K. Vamanamurthy and M. Vuorinen, Functional inequalities, Jacobi products and quasiconformal maps, Illinois J. Math. 38 (1994), 394-419.