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Grstzsch环与Ramanujan的模方程
Grtzsck Ring and Ramanujan’s Modular Equations
【摘要】 本文建立了拟共形映照理论中平面Grtzsch环的模μ(r)与由(8)式定义的出现于数论中Ramanujan广义模方程的函数μa(γ)之间的关系,并将μ(γ)的若干已知结果推广到μa(γ);为研究模方程理论提供了一种方法.
【Abstract】 The author establishes the connection between the modulusμ(γ) of the plane Grtzsch ring and its generalizationμa(γ), which appears in Ramanujan’s generalized modular equation, and extends several well-known results forμ(γ) toμa(γ), thus providing a method for the study of the modular equations.
【关键词】 拟共形理论;
Grtzsch环;
Ramanujan的模方程;
Gauss超几何函数;
【Key words】 Quasiconformal theory; Grtzsch ring; Ramanujan’s modular equation; Gaussian hypergeometric function;
【Key words】 Quasiconformal theory; Grtzsch ring; Ramanujan’s modular equation; Gaussian hypergeometric function;
【基金】 芬兰科学院科学基金
- 【文献出处】 数学学报 ,ACTA MATHEMATICA SINICA , 编辑部邮箱 ,2000年02期
- 【分类号】O153
- 【被引频次】31
- 【下载频次】85