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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
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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] L.GERRITZEN AND M.VAN DER PUT, Schottky groups and Mumford curves, Lecture Notes in Math. 817(1980), Springer. MR 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.

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Additional Information

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

Masaaki Yoshida
Affiliation: Department of Mathematics, Kyushu University, Fukuoka 810-8560 Japan

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

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