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Grötzsch ring and Ramanujan’s modular equations. (Chinese. English summary) Zbl 1005.11013

Summary: The author establishes the connection between the modulus \(\mu(r)\) of the plane Grötzsch ring and its generalization \(\mu_a(r)\), which appears in Ramanujan’s generalized modular equation, and extends several well-known results for \(\mu(r)\) to \(\mu_a(r)\), thus providing a method for the study of the modular equations.

MSC:

11F03 Modular and automorphic functions
30C62 Quasiconformal mappings in the complex plane
33C05 Classical hypergeometric functions, \({}_2F_1\)
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