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A family of Schottky groups arising from the hypergeometric equation

Authors: Takashi Ichikawa and Masaaki Yoshida
Journal: Proc. Amer. Math. Soc. 134 (2006), 2271-2280
MSC (2000): Primary 33C05, 30F10, 30F40
Published electronically: February 2, 2006
MathSciNet review: 2213699
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Abstract: We study a complex 3-dimensional family of classical Schottky groups of genus 2 as monodromy groups of the hypergeometric equation. We find non-trivial loops in the deformation space; these correspond to continuous integer-shifts of the parameters of the equation.

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  • [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, 1994).
  • [GP] L.GERRITZEN AND M.VAN DER PUT, Schottky groups and Mumford curves, Lect. Notes in Math. 817(1980) Springer. MR 0590243 (82j:10053)
  • [IY] T. ICHIKAWA AND M.YOSHIDA, On Schottky groups arising from the hypergeometric equation with imaginary exponents, Proc AMS 132(2003), 447-454. MR 2022368
  • [IKSY] K.IWASAKI, H.KIMURA, S.SHIMOMURA AND M.YOSHIDA, From Gauss to Painlevé - A modern theory of special functions, Vieweg Verlag, Wiesbaden, 1991. MR 1118604 (92j:33001)
  • [Gray] J. GRAY, Linear differential equations and group theory from Riemann to Poincaré, Birkhäuser, 2000. MR 1751835 (2000m:34002)
  • [MSW] D. MUMFORD, C. SERIES AND D. WRIGHT, Indra's Pearls, Cambridge Univ. Press, 2002. MR 1913879 (2003f:00005)
  • [SY] T.SASAKI AND M.YOSHIDA, A geometric study of the hypergeometric function with imaginary exponents, Experimental Math. 10(2000), 321-330. MR 1917420 (2003f:33002)
  • [Sch] 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, Schottky group
Received by editor(s): October 1, 2004
Received by editor(s) in revised form: February 24, 2005
Published electronically: February 2, 2006
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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