模方程与偏差函数
Modular Equations and Distortion Functions
摘要：
模方程出现在数论中，但较少有人知道这类方程也出现在拟共形映射变形性质的研究中。研究了两个重要的平面拟共形偏差函数，得到了它们的单调性和凸性，并找到了它们的精确界。应用程序提供有关的拟共形Schwarz引理和肖特基定理。这些结果也给出了完全椭圆积分奇异值的新的界。
英文摘要：
Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions, obtaining monotonicity and convexity properties, and finding sharp bounds for them. Applications are provided that relate to the quasiconformal Schwarz Lemma and to Schottky's Theorem. These results also yield new bounds for singular values of complete elliptic integrals.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
