  {\em The Liouville number}, denoted $l$, is defined by
$$l:=0.100101011101101111100...,$$ where the $n$th bit is given by
${1/2}(1+\gl(n))$; here $\gl$ is the Liouville function for the parity of prime
divisors of $n$. Presumably the Liouville number is transcendental, though at
present, a proof is unattainable. Similarly, define {\em the Gaussian Liouville
number} by $$\gamma:=0.110110011100100111011...$$ where the $n$th bit reflects
the parity of the number of rational Gaussian primes dividing $n$, 1 for even
and 0 for odd.
  In this paper, we prove that the Gaussian Liouville number and its relatives
are transcendental. One such relative is the number
$$\sum_{k=0}^\infty\frac{2^{3^k}}{2^{3^k2}+2^{3^k}+1}=0.101100101101100100101...,$$
where the $n$th bit is determined by the parity of the number of prime divisors
that are equivalent to 2 modulo 3.
  We use methods similar to that of Dekking's proof of the transcendence of the
Thue--Morse number \cite{Dek1} as well as a theorem of Mahler's \cite{Mahl1}.
(For completeness we provide proofs of all needed results.) This method
involves proving the transcendence of formal power series arising as generating
functions of completely multiplicative functions.
