Algebraic Values of Schwarz Triangle Functions

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


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.


Schwarz triangle functions hypergeometric functions algebraic values transcendence complex multiplication 


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© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  1. 1.Inst. of Math. and PhysicsChiba UniversityChibaJapan
  2. 2.Math. Sem. der Univ.Frankfurt a.M.Germany

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