Quantitative steps in the Axer–Landau equivalence theorem
Volume 187 / 2019
Acta Arithmetica 187 (2019), 345-355
MSC: 11M06, 11N56, 11N80.
DOI: 10.4064/aa170424-13-5
Published online: 25 January 2019
Abstract
Completing previous enquiries of the same nature, it is shown that, for every non-negative integer $h$, there exists a positive constant $c$ such that $|\sum_{n\le x}\mu(n)(\log n)^h/n|\ll \max_{y\sim x}|\sum_{n\le y}\mu(n)|(\log y)^h/y+x^{-c/\!\log\log x}$ for $x\ge10$. The main theorem applies to general problems of this kind.
