Algebraic values of Schwarz triangle functions

We consider Schwarz maps for triangles whose angles are rather general rational multiples of pi. Under which conditions can they have algebraic values at algebraic arguments? The answer is based mainly on considerations 
We consider Schwarz maps for triangles whose angles are rather general rational multiples of pi. 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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Metadaten
Author:Hironori Shiga, Jürgen Wolfart
URN:urn:nbn:de:hebis:30-11852
Document Type:Report
Language:English
Date of Publication (online):2005/06/29
Year of first Publication:2005
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2005/06/29
Tag:Schwarz triangel functions ; algebraic values ; complex multiplication; hypergeometric functions ; transcendence
Note:
auch in: Technical Reports of Mathematical Sciences, Chiba University, 20 (2004), No. 5. Revised and extended version erscheint in den Proceedings der CIMPA Summer School AGAHF, Istanbul 2005.
Source:http://www.math.uni-frankfurt.de/~wolfart/wolfart.html , Technical Reports of Mathematical Sciences, Chiba University, 20 (2004), No. 5. Revised and extended version erscheint in den Proceedings der CIMPA Summer School AGAHF, Istanbul 2005.
HeBIS PPN:432312889
Institutes:Mathematik
Dewey Decimal Classification:510 Mathematik
MSC-Classification:11J91 Transcendence theory of other special functions
11J95 Results involving abelian varieties
14K22 Complex multiplication [See also 11G15]
30C20 Conformal mappings of special domains
33C05 Classical hypergeometric functions, 2F1
Sammlungen:Universitätspublikationen
Licence (German):License Logo Veröffentlichungsvertrag für Publikationen

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