English

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}
}
R2 v1 2026-06-21T13:01:43.264Z