TY  - RPRT
A1  - Shiga, Hironori
A1  - Wolfart, Jürgen
T1  - Algebraic values of Schwarz triangle functions
N2  - 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.
KW  - Schwarz triangel functions
KW  - hypergeometric functions
KW  - algebraic values
KW  - transcendence
KW  - complex multiplication
Y1  - 2005
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/4306
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30-11852
UR  - http://www.math.uni-frankfurt.de/~wolfart/wolfart.html
N1  - 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.
ER  -