Asymptotic Estimates for Some Number Theoretic Power Series
arXiv:0905.2070 · doi:10.4064/aa142-2-8
Abstract
We derive asymptotic bounds for the ordinary generating functions of several classical arithmetic functions, including the Moebius, Liouville, and von Mangoldt functions. The estimates result from the Korobov-Vinogradov zero-free region for the Riemann zeta-function, and are sharper than those obtained by Abelian theorems from bounds for the summatory functions.