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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
Posted:
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.
References
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L.GERRITZEN AND M.VAN DER PUT, Schottky groups and Mumford curves, Lect. Notes in Math. 817(1980) Springer. MR 0590243 (82j:10053)
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T. ICHIKAWA AND M.YOSHIDA, On Schottky groups arising from the hypergeometric equation with imaginary exponents, Proc AMS 132(2003), 447-454. MR 2022368
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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)
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J. GRAY, Linear differential equations and group theory from Riemann to Poincaré, Birkhäuser, 2000. MR 1751835 (2000m:34002)
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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
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/S0002-9939-06-08235-9
PII:
S 0002-9939(06)08235-9
Keywords:
Hypergeometric equation,
monodromy group,
Schottky group
Received by editor(s):
October 1, 2004
Received by editor(s) in revised form:
February 24, 2005
Posted:
February 2, 2006
Communicated by:
Carmen C. Chicone
Article copyright:
© Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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