On the Behavior of a Power Series with Completely Multiplicative Coefficients near the Unit Circle

Power series whose coefficients are values of completely multiplicative functions from a general class determined by a small number of constraints are studied. The paper contains proofs of asymptotic estimates as such a power series tends to the roots of $1$ along the radii of the unit circle, whence, in particular, it follows that these series cannot be extended beyond the unit disk.