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Quantitative steps in the Axer–Landau equivalence theorem

Volume 187 / 2019

O. Ramaré Acta Arithmetica 187 (2019), 345-355 MSC: 11M06, 11N56, 11N80. DOI: 10.4064/aa170424-13-5 Published online: 25 January 2019


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.


  • O. RamaréCNRS / Institut de Mathématiques de Marseille
    Aix Marseille Université, U.M.R. 7373
    Site Sud, Campus de Luminy, Case 907
    13288 Marseille Cedex 9, France

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