Algebraic Values of Schwarz Triangle Functions

Hironori Shiga, Jürgen Wolfart

Type: Book-Chapter

Publication Date: 2007-06-27

Citations: 5

DOI: https://doi.org/10.1007/978-3-7643-8284-1_11

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.

Locations

Publication Server of Goethe University Frankfurt am Main (Goethe University Frankfurt) - View - PDF
Birkhäuser Basel eBooks - View

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