The theory of Liouville functions

Abstract : A Liouville function is a complex analytic function H with a Taylor series ∑∞n=1xn/an such the a_n's form a ``very fast growing'' sequence of integers. In this paper we exhibit the complete first-order theory of the complex field expanded with H.
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Pascal Koiran. The theory of Liouville functions. [Research Report] LIP RR-2002-13, Laboratoire de l'informatique du parallélisme. 2002, 2+14p. ⟨hal-02101875⟩

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