Abstract
The aim of this paper is to prove that the strings of 0 in the β-expansion of 1 exhibit a lacunarity bounded by a quantity related to the absolute value of the conjugate of β when β is an algebraic power series over the finite field Fq with |β|>1. This result provides, in a natural way, a family of transcendental power series β such that dβ(1) is not q-automatic.
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