On Schottky groups arising from the hypergeometric equation with imaginary exponents-Reference-Cited by-同舟云学术

On Schottky groups arising from the hypergeometric equation with imaginary exponents

Published:2003-06-12 Issue:2 Volume:132 Page:447-454
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Ichikawa Takashi,Yoshida Masaaki

Abstract

In an article by Sasaki and Yoshida (2000), we encountered Schottky groups of genus 2 as monodromy groups of the hypergeometric equation with purely imaginary exponents. In this paper we study automorphic functions for these Schottky groups, and give a conjectural infinite product formula for the elliptic modular function λ \lambda .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2004-132-02/S0002-9939-03-07117-X/S0002-9939-03-07117-X.pdf

Reference4 articles.

1. [BBEIM] E.D.Belokolos, A.I.Bobenko, V.Z.Enol’skii, A.R.Its and V.B.Matveev, Algebro-geometric Approach to Nonlinear Integrable Equations, Springer Series in Nonlinear Dynamics, Springer-Verlag, New York, 1994.

2. Über die Teilbarkeitsbedingungen bei den gewöhnlichen Differential polynomen;Rádl, Franz;Math. Z.,1939

3. [SY] T.Sasaki and M.Yoshida, A geometric study of the hypergeometric function with imaginary exponents, Experimental Math. 10(2000), 321–330.

4. [S] F.Schottky, Über eine specielle Function, welche bei einer bestimmten linearen Transformation ihres Arguments univerändert bleibt, J. Reine Angew. Math. 101(1887) 227–272.

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