ARITHMETIC PROPERTIES OF SCHWARZ MAPS

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概要

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• We consider a non-algebraic Schwarz map D for the hypergeometric differential equation of Appell-Lauricella type with rather general rational parameters. Under which conditions can D take algebraic values at algebraic vector arguments τ ? As a necessary condition, the canonical Prym variety lying in the Jacobian of the hypergeometric curve belonging to τ must have a factor with complex multiplication. However, it will be shown that in a Zariski dense subset of arguments few contiguous Schwarz maps D can take algebraic values D(τ) even if this CM condition is satisfied. Explicit examples show that there are exceptional arguments where this statement fails.

著者

• SUZUKI Yoshio

  Institute of Mathematics and Physics Chiba University

• SHIGA Hironori

  Institute of Mathematics and Physics Chiba University

• Wolfart Jürgen

  Math. Seminar der Univ.

関連論文

• Magnetic Properties of Fe_3 Pt Invar Alloys in High Magnetic Fields
• ARITHMETIC PROPERTIES OF SCHWARZ MAPS

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