On Schwarzian Triangle Functions, Automorphic Forms and a Generalization of Ramanujan’s Triple Differential Equations

On Schwarzian Triangle Functions, Automorphic Forms and a Generalization of Ramanujan’s Triple... Let G be the group of the fractional linear transformations generated by $$T(\tau ) = \tau + \lambda ,S(\tau ) = \frac{{\tau \cos \frac{\pi }{n} + \sin \frac{\pi }{n}}}{{ - \tau \sin \frac{\pi }{n} + \cos \frac{\pi }{n}}};$$ T ( τ ) = τ + λ , S ( τ ) = τ cos π n + sin π n − τ sin π n + cos π n ; where $$\lambda = 2\frac{{\cos \frac{\pi }{m} + \cos \frac{\pi }{n}}}{{\sin \frac{\pi }{n}}};$$ λ = 2 cos π m + cos π n sin π n ; m, n is a pair of integers with either n ≥ 2,m ≥ 3 or n ≥ 3,m ≥ 2; τ lies in the upper half plane H. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematica Sinica, English Series Springer Journals

On Schwarzian Triangle Functions, Automorphic Forms and a Generalization of Ramanujan’s Triple Differential Equations

Acta Mathematica Sinica, English Series, Volume 34 (11) – May 7, 2018
15 pages

Publisher
Springer Journals
Copyright © 2018 by Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
1439-8516
eISSN
1439-7617
DOI
10.1007/s10114-018-6389-2
Publisher site
See Article on Publisher Site

Abstract

Let G be the group of the fractional linear transformations generated by $$T(\tau ) = \tau + \lambda ,S(\tau ) = \frac{{\tau \cos \frac{\pi }{n} + \sin \frac{\pi }{n}}}{{ - \tau \sin \frac{\pi }{n} + \cos \frac{\pi }{n}}};$$ T ( τ ) = τ + λ , S ( τ ) = τ cos π n + sin π n − τ sin π n + cos π n ; where $$\lambda = 2\frac{{\cos \frac{\pi }{m} + \cos \frac{\pi }{n}}}{{\sin \frac{\pi }{n}}};$$ λ = 2 cos π m + cos π n sin π n ; m, n is a pair of integers with either n ≥ 2,m ≥ 3 or n ≥ 3,m ≥ 2; τ lies in the upper half plane H.

Journal

Acta Mathematica Sinica, English SeriesSpringer Journals

Published: May 7, 2018

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