On Schottky groups arising from the hypergeometric equation with imaginary exponents
HTML articles powered by AMS MathViewer
- by Takashi Ichikawa and Masaaki Yoshida PDF
- Proc. Amer. Math. Soc. 132 (2004), 447-454 Request permission
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 $\lambda$.References
- 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.
- Franz Rádl, Über die Teilbarkeitsbedingungen bei den gewöhnlichen Differential polynomen, Math. Z. 45 (1939), 429–446 (German). MR 82, DOI 10.1007/BF01580293
- T. Sasaki and M. Yoshida, A geometric study of the hypergeometric function with imaginary exponents, Experimental Math. 10(2000), 321–330.
- F. Schottky, Über eine specielle Function, welche bei einer bestimmten linearen Transformation ihres Arguments univerändert bleibt, J. Reine Angew. Math. 101(1887) 227–272.
Additional Information
- Takashi Ichikawa
- Affiliation: Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga 840-8502 Japan
- MR Author ID: 253584
- Email: ichikawa@ms.saga-u.ac.jp
- Masaaki Yoshida
- Affiliation: Department of Mathematics, Kyushu University, Fukuoka 810-8560 Japan
- Email: myoshida@math.kyushu-u.ac.jp
- Received by editor(s): October 1, 2001
- Received by editor(s) in revised form: October 2, 2002
- Published electronically: June 12, 2003
- Communicated by: Carmen C. Chicone
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 447-454
- MSC (2000): Primary 33C05
- DOI: https://doi.org/10.1090/S0002-9939-03-07117-X
- MathSciNet review: 2022368