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Algebraic Values of Schwarz Triangle Functions

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Arithmetic and Geometry Around Hypergeometric Functions

Part of the book series: Progress in Mathematics ((PM,volume 260))

Abstract

We consider Schwarz maps for triangles whose angles are rather general rational multiples of π. Under which conditions can they have algebraic values at algebraic arguments? The answer is based mainly on considerations of complex multiplication of certain Prym varieties in Jacobians of hypergeometric curves. The paper can serve as an introduction to transcendence techniques for hypergeometric functions, but contains also new results and examples.

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Author information

Authors and Affiliations

  1. Inst. of Math. and Physics, Chiba University, Yayoi-cho 1-33, Inage-ku, Chiba, 263-8522, Japan

    Hironori Shiga

  2. Math. Sem. der Univ., Postfach 111932, D-60054, Frankfurt a.M., Germany

    Jürgen Wolfart

Authors
  1. Hironori Shiga
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  2. Jürgen Wolfart
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Editor information

Editors and Affiliations

  1. Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099, Berlin

    Rolf-Peter Holzapfel

  2. Department of Mathematics, Galatasaray University, 34357, Besiktas, Istanbul, Turkey

    A. Muhammed Uludağ

  3. Department of Mathematics, Kyushu University, Fukuoka, 810-8560, Japan

    Masaaki Yoshida

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© 2007 Birkhäuser Verlag Basel/Switzerland

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Shiga, H., Wolfart, J. (2007). Algebraic Values of Schwarz Triangle Functions. In: Holzapfel, RP., Uludağ, A.M., Yoshida, M. (eds) Arithmetic and Geometry Around Hypergeometric Functions. Progress in Mathematics, vol 260. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8284-1_11

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