On the expansion of some exponential periods in an integer base

Boris Adamczewski (1)

1 ICJ - Institut Camille Jordan

We derive a lower bound for the subword complexity of the base-b expansion (b a parts per thousand yen 2) of all real numbers whose irrationality exponent is equal to 2. This provides a generalization of a theorem due to Ferenczi and Mauduit. As a consequence, we obtain the first lower bound for the subword complexity of the number e and of some other transcendental exponential periods.

Domaines: Théorie des nombres [math.NT]

Boris Adamczewski. On the expansion of some exponential periods in an integer base. Mathematische Annalen, 2010, 346, pp.107-116. ⟨10.1007/s00208-009-0391-z⟩. ⟨hal-00863633⟩