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arXiv · 0905.2070

Asymptotic Estimates for Some Number Theoretic Power Series

Stefan Gerhold
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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.

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Stefan Gerhold. 2009-05-13. Asymptotic Estimates for Some Number Theoretic Power Series. https://doi.org/10.4064/aa142-2-8

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