  We give a new proof of Fatou's theorem: {\em if an algebraic function has a
power series expansion with bounded integer coefficients, then it must be a
rational function.} This result is applied to show that for any non--trivial
completely multiplicative function from $\mathbb{N}$ to $\{-1,1\}$, the series
$\sum_{n=1}^\infty f(n)z^n$ is transcendental over $\mathbb{Z}[z]$; in
particular, $\sum_{n=1}^\infty \lambda(n)z^n$ is transcendental, where
$\lambda$ is Liouville's function. The transcendence of $\sum_{n=1}^\infty
\mu(n)z^n$ is also proved.
