A1 Refereed original research article in a scientific journal
Modular equations and distortion functions
Authors: Anderson G., Qiu S., Vuorinen M.
Publication year: 2009
Journal: Ramanujan Journal
Journal name in source: Ramanujan Journal
Volume: 18
Issue: 2
First page : 147
Last page: 169
Number of pages: 23
ISSN: 1382-4090
DOI: https://doi.org/10.1007/s11139-007-9047-3
Web address : http://api.elsevier.com/content/abstract/scopus_id:59949105352
Abstract
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. © 2007 Springer Science+Business Media, LLC.
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. © 2007 Springer Science+Business Media, LLC.
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