广义GrO<sup style=" margin-left:-7px;">¨</sup>tzsch环函数的精确界及应用

Sharp Inequalities and Application of the Generalized GrO<sup style=" margin-left:-7px;">¨</sup>tzsch Ring Function

本文研究广义Grotzsch环函数与一些初等函数组合的单调性,并由此获得新的精确不等式。同时,将所得结果应用于Ramanujan模方程理论,获得广义Hersch-Pfluger偏差函数新的下界。

In this paper,we study some monotonicity properties of certain functions defined in term of gen-eralized Gr&#246;tzsch ring function and some elementary functions,and get new sharp inequalities.Furthermore,we also obtain the lower bound of generalized Hersch-Pfluger distortion function by applying these results in Ramanujan modular equation theory.