Zariski-density of exceptional sets for hypergeometric functions Academic Article uri icon

abstract

  • We extend the results of Desrousseaux in [10], [11], [12]. 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 André-Oort conjecture. In this paper, we show that generalizations of the André-Oort conjecture by Pink [20] 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.

citation count

  • 2

publication date

  • January 2008