Some properties and asymptotically sharp bounds are obtained for singdar values of Ramanujan’s generalized modular equation. from which infinite-product representations of the Hersch-Pfluger ?dimtortion function ? K ...Some properties and asymptotically sharp bounds are obtained for singdar values of Ramanujan’s generalized modular equation. from which infinite-product representations of the Hersch-Pfluger ?dimtortion function ? K (r) and the Agard η-distortion function η K (t) follow. By these results, the explicit quasiconformal Schwan lemma is improved, several properties are obtained for the Schottky upper bound, and a conjecture on the linear distortion function λ (K) is proved to be true.展开更多
文摘Some properties and asymptotically sharp bounds are obtained for singdar values of Ramanujan’s generalized modular equation. from which infinite-product representations of the Hersch-Pfluger ?dimtortion function ? K (r) and the Agard η-distortion function η K (t) follow. By these results, the explicit quasiconformal Schwan lemma is improved, several properties are obtained for the Schottky upper bound, and a conjecture on the linear distortion function λ (K) is proved to be true.
