We derive asymptotic bounds for the ordinary generating functions of several classical arithmetic functions, including the Möbius, Liouville, and von Mangoldt functions. The estimates result from the KorobovVinogradov zero-free region for the Riemann zeta-function, and are sharper than those obtained by Abelian theorems from bounds for the summatory functions. Such functions as P μ(n)x, P φ(n)x...