Asymptotic Estimates for Some Number Theoretic Power Series
نویسنده
چکیده
We derive asymptotic bounds for the ordinary generating functions of several classical arithmetic functions, including the Möbius, Liouville, and von Mangoldt functions. The estimates result from the KorobovVinogradov zero-free region for the Riemann zeta-function, and are sharper than those obtained by Abelian theorems from bounds for the summatory functions. Such functions as P μ(n)x, P φ(n)x, P Λ(n)x are extremely difficult to handle. — G.H. Hardy, E.M. Wright [15]
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تاریخ انتشار 2009