Qiu, Songliang Grötzsch ring and Ramanujan’s modular equations. (Chinese. English summary) Zbl 1005.11013 Acta Math. Sin. 43, No. 2, 283-290 (2000). 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. Cited in 20 Documents MSC: 11F03 Modular and automorphic functions 30C62 Quasiconformal mappings in the complex plane 33C05 Classical hypergeometric functions, \({}_2F_1\) Keywords:quasiconformal theory; Ramanujan’s modular equation; Gaussian hypergeometric function; Grötzsch ring PDFBibTeX XMLCite \textit{S. Qiu}, Acta Math. Sin. 43, No. 2, 283--290 (2000; Zbl 1005.11013)