Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On Schottky groups arising from the hypergeometric equation with imaginary exponents


Authors: Takashi Ichikawa and Masaaki Yoshida
Journal: Proc. Amer. Math. Soc. 132 (2004), 447-454
MSC (2000): Primary 33C05
Published electronically: June 12, 2003
MathSciNet review: 2022368
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [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.
  • [GP] Lothar Gerritzen and Marius van der Put, Schottky groups and Mumford curves, Lecture Notes in Mathematics, vol. 817, Springer, Berlin, 1980. MR 590243 (82j:10053)
  • [SY] T.SASAKI AND M.YOSHIDA, A geometric study of the hypergeometric function with imaginary exponents, Experimental Math. 10(2000), 321-330.
  • [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.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 33C05

Retrieve articles in all journals with MSC (2000): 33C05


Additional Information

Takashi Ichikawa
Affiliation: Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga 840-8502 Japan
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

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07117-X
PII: S 0002-9939(03)07117-X
Keywords: Hypergeometric equation, monodromy group, Schwarzian derivative, reflection principle, Schottky group, automorphic functions, infinite product, $\lambda$ function.
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
Article copyright: © Copyright 2003 American Mathematical Society