Asymptotic Estimates for Some Number Theoretic Power Series
Number Theory
2015-05-13 v1 Combinatorics
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.
Keywords
Cite
@article{arxiv.0905.2070,
title = {Asymptotic Estimates for Some Number Theoretic Power Series},
author = {Stefan Gerhold},
journal= {arXiv preprint arXiv:0905.2070},
year = {2015}
}