Asymptotic Estimates for Some Number Theoretic Power Series

Details Asymptotic Estimates for Some Number Theoretic Power Series Asymptotic Estimates for Some Number Theoretic Power Series

2009-05-13

arxiv.org/abs/0905.2070v1

Mathematics

Number Theory

Scientific paper

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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