Zariski-density of exceptional sets for hypergeometric functions
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We extend the results of Desrousseaux in , , . In those papers an exceptional set was constructed for the Appell-Lauricella hypergeometric functions associated to rational ball tuples. The definition of this set requires quite subtle conditions necessary for the application of the Andr-Oort conjecture. In this paper, we show that generalizations of the Andr-Oort conjecture by Pink  lead to similar results for a more natural exceptional set, namely the set of algebraic points at which the function takes algebraic values. Desrousseaux's exceptional set is in general a proper subset of this set. Walter de Gruyter 2008.
author list (cited authors)
Desrousseaux, P., Tretkoff, M. D., & Tretkoff, P.
complete list of authors
Desrousseaux, Pierre-Antoine||Tretkoff, Marvin D||Tretkoff, Paula